• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.21-38
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• 2004

We prove that a Banach space that is convex-transitive and such that for some element u in the unit sphere, and for every subspace Μ containing u, it happens that the subset of norm attaining functionals on Μ is second Baire category in $M^{*}$ is, in fact, almost-transitive and superreflexive. We also obtain a characterization of finite-dimensional spaces in terms of functions that attain their supremum: a Banach space is finite-dimensional if, for every equivalent norm, every rank-one operator attains its numerical radius. Finally, we describe the subset of norm attaining functionals on a space isomorphic to $\ell$$_1$, where the norm is the restriction of a Luxembourg norm on $L_1$. In fact, the subset of norm attaining functionals for this norm coincides with the subset of norm attaining functionals for the usual norm.m.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.173-180
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• 1994

Let H be a separable, infinite dimensional, compled Hilbert space and let L(H) be the algebra of all bounded linear operators on H. A dual algebra is a subalgebra of L(H) that contains the identity operator $I_{H}$ and is closed in the ultraweak topology on L(H). Note that the ultraweak operator topology coincides with the wea $k^{*}$ topology on L(H)(see [3]). Bercovici-Foias-Pearcy [3] studied the problem of solving systems of simultaneous equations in the predual of a dual algebra. The theory of dual algebras has been applied to the topics of invariant subspaces, dilation theory and reflexibity (see [1],[2],[3],[5],[6]), and is deeply related with properties ( $A_{m,n}$). Jung-Lee-Lee [7] introduced n-separating sets for subalgebras and proved the relationship between n-separating sets and properties ( $A_{m,n}$). In this paper we will study the relationship between direct sum and properties ( $A_{m,n}$). In particular, using some results of [7] we obtain relationship between n-separating sets and direct sum of von Neumann algebras.ras.s.ras.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.785-827
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• 2023

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with a P-accretive mapping, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the construction of a new iterative algorithm using the resolvent operator technique and Nadler's technique for solving a new system of generalized multi-valued resolvent equations in a Banach space setting. The convergence analysis of the sequences generated by our proposed iterative algorithm under some appropriate conditions is studied. The final section deals with the investigation and analysis of the notion of H(·, ·)-co-accretive mapping which has been recently introduced and studied in the literature. We verify that under the conditions considered in the literature, every H(·, ·)-co-accretive mapping is actually P-accretive and is not a new one. In the meanwhile, some important comments on H(·, ·)-co-accretive mappings and the results related to them appeared in the literature are pointed out.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1241-1257
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• 2014

We consider a class of hypoelliptic operators of the following type $$L=\sum_{i,j=1}^{p_0}a_{ij}{\partial}^2_{x_ix_j}+\sum_{i,j=1}^{N}b_{ij}x_i{\partial}_{x_j}-{\partial}_t$$, where ($a_{ij}$), ($b_{ij}$) are constant matrices and ($a_{ij}$) is symmetric positive definite on $\mathbb{R}^{p_0}$ ($p_0{\leqslant}N$). By establishing global Morrey estimates of singular integral on the homogenous space and the relation between Morrey space and weak Morrey space, we obtain the global weak Morrey estimates of the operator L on the whole space $\mathbb{R}^{N+1}$.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.25 no.6
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• pp.492-497
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• 2016

Teaching an industrial robot is still a dangerous and time-consuming process. It is expected that a robot can track a trajectory that is repeatedly taught by a human operator. Teaching a robot in joint space is easier than that in Cartesian space or a work space because the robot will never lose its stability when it is taught and operated in a joint space. However, it is very easy for a robot to lose its stability when it is taught in a work space. This is because of the singular points problem in kinematics for manipulators. Thus, experts should teach a given task to a robot in a careful manner. A new algorithm that avoids the problem of singular points is proposed. Using this proposed method, a user can freely teach a robot without the chance of instability in an entire work space.

• The Korean Journal of Air & Space Law and Policy
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• v.33 no.2
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• pp.367-418
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• 2018

Just as safety is the most important thing in aviation, safety is the most important in the operation of unmanned aircraft (RPA), and safety operation is the most important in the legal responsibility of the operator of the unmanned aircraft. In this thesis, the legal responsibility of the operator of the unmanned aircraft, focusing on the responsibility of the operator of the unmanned aircraft, was discussed in depth with the issue of insurance, which compensates for damages in the event of an accident First of all, the legal responsibility of the operator of the unmanned aircraft was reviewed for the most basic : definition, scope and qualification of the operator of the unmanned aircraft, and the liability of the operator of the Convention On International Civil Aviation, the ICAO Annex, the RPAS Manual, the Rome Convention, other major international treaties and Domestic law such as the Aviation Safety Act. The ICAO requires that unmanned aircraft be operated in such a manner as to minimize hazards to persons, property or other aircraft as a major principle of the operation of unmanned aircraft, which is ultimately equivalent to manned aircraft Considering that most accidents involving unmanned aircrafts fall to the ground, causing damage to third parties' lives or property, this thesis focused on the responsibility of operators under the international treaty, and the responsibility of third parties for air transport by Domestic Commercial Act, as well as the liability for compensation. In relation to the Rome Convention, the Rome Convention 1952 detailed the responsibilities of the operator. Although it has yet to come into effect regarding liability, some EU countries are following the limit of responsibility under the Rome Convention 2009. Korea has yet to sign any Rome Convention, but Commercial Act Part VI Carriage by Air is modeled on the Rome Convention 1978 in terms of compensation. This thesis also looked at security-related responsibilities and the responsibility for privacy infringement. which are most problematic due to the legal responsibilities of operating unmanned aircraft. Concerning insurance, this thesis looked at the trends of mandatory aviation insurance coverage around the world and the corresponding regulatory status of major countries to see the applicability of unmanned aircraft. It also looked at the current clauses of the Domestic Aviation Business Act that make insurance mandatory, and the ultra-light flight equipment insurance policy and problems. In sum, the operator of an unmanned aircraft will be legally responsible for operating the unmanned aircraft safely so that it does not pose a risk to people, property or other aircraft, and there will be adequate compensation in the event of an accident, and legal systems such as insurance systems should be prepared to do so.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.205-209
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• 2011

Let $\mathcal{QA}$ denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality $T^*|T^2|T{\geq}T^*|T|^2T$. Let $f$ be an analytic function defined on an open neighbourhood $\mathcal{U}$ of ${\sigma}(T)$ such that $f$ is non-constant on the connected components of $\mathcal{U}$. We generalize a theorem of Sheth [10] to $f(T){\in}\mathcal{QA}$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.367-373
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• 2007

For a unital *-subalgebra of the space $\mathcal{L}^a(X)$ of all adjointable maps on a Hilbert $\mathcal{B}$-module X with a $C^*$-algebra $\mathcal{B}$, we study unitary operator (in such algebra)-valued multiplier ${\sigma}$ on a normal, generating subsemigroup S of a group G with its extension to G. A dilation of a projective isometric ${\sigma}$-representation of S is established as a projective unitary ${\rho}$-representation of G for a suitable unitary operator (in some algebra)-valued multiplier ${\rho}$ associated with the multiplier ${\sigma}$ which is explicitly constructed.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.385-397
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• 2003

In this paper, we introduce and study a system of nonlinear implicit variational inclusions (SNIVI) in real Banach spaces: determine elements $x^{*},\;y^{*},\;z^{*}\;\in\;E$ such that ${\theta}\;{\in}\;{\alpha}T(y^{*})\;+\;g(x^{*})\;-\;g(y^{*})\;+\;A(g(x^{*}))\;\;\;for\;{\alpha}\;>\;0,\;{\theta}\;{\in}\;{\beta}T(z^{*})\;+\;g(y^{*})\;-\;g(z^{*})\;+\;A(g(y^{*}))\;\;\;for\;{\beta}\;>\;0,\;{\theta}\;{\in}\;{\gamma}T(x^{*})\;+\;g(z^{*})\;-\;g(x^{*})\;+\;A(g(z^{*}))\;\;\;for\;{\gamma}\;>\;0,$ where T, g : $E\;{\rightarrow}\;E,\;{\theta}$ is zero element in Banach space E, and A : $E\;{\rightarrow}\;{2^E}$ be m-accretive mapping. By using resolvent operator technique for n-secretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this system of nonlinear implicit variational inclusions. The convergence of iterative algorithms be proved in q-uniformly smooth Banach spaces and in real Banach spaces, respectively.