• Korean Journal of Mathematics
• /
• v.25 no.2
• /
• pp.247-259
• /
• 2017

By the use of inequalities for nonnegative Hermitian forms some new inequalities for numerical radius of bounded linear operators in complex Hilbert spaces are established.

• Kyungpook Mathematical Journal
• /
• v.47 no.2
• /
• pp.253-265
• /
• 2007

In this paper, the boundedness for some multilinear operators generated by singular integralv operators and Lipschitz functions on Hardy and Herz-type spaces are obtained.

• Communications of the Korean Mathematical Society
• /
• v.19 no.3
• /
• pp.461-467
• /
• 2004

In this paper, we study the Ishikawa iterative sequences with errors for Lipschitzian strongly pseudo-contractive operator in arbitrary real Banach spaces. Our results improve the results obtained previously by C. E. Chidume [3] and Zeng [9].

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.609-617
• /
• 2019

We characterize two-point homogeneous spaces M by means of the structural operator $h={\frac{1}{2}}{\mathcal{L}}_{\xi}{\phi}$ or the characteristic Jacobi operator ${\ell}=R({\cdot},{\xi}){\xi}$ on the unit tangent sphere bundles $T_1M$.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.187-200
• /
• 2019

Truncated Hankel operators are compressions of classical Hankel operators to model spaces. In this paper we describe matrix representations of truncated Hankel operators on finite-dimensional model spaces. We then show that the obtained descriptions hold also for some infinite-dimensional cases.

• Honam Mathematical Journal
• /
• v.42 no.4
• /
• pp.811-819
• /
• 2020

We give characterizations of locally symmetric spaces M via the structural operator $h={\frac{1}{2}{\mathcal{L}}_{\xi}{\phi}}$ or the characteristic Jacobi operator ℓ = R(·, ξ)ξ on the unit tangent sphere bundles T1M.

• Bulletin of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.27-30
• /
• 1984

The concepts of the numerical range of an operator on a Hillbert space and on a Banach space were introduced by Toeplitz in 1918 and Bauer in 1962 respectively. Bauer's paper was concerned only with finite dimensional Banach spaces, but the concept of numerical range that he introduced is available without restriction of the dimension [1, 2]. In this paper, we define a C-algebra spatial numerical range of an operator on C-algebra valued inner product modules introduced by Paschke [4], and give analogous results on these modules as those on Banach spaces.

• Journal of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.205-216
• /
• 1996

In [13], Ptak and Vrbova proved that if T is a bounded normal operator T on a complex Hilbert space H, then the ranges of the spectral projections can be represented in the form $$ \varepsilon(F)H = \bigcap_{\lambda\notinF} (T - \lambda I) H for all closed subsets F of C, $$ where $\varepsilon$ denotes the spectral measure associated with T.

• Communications of the Korean Mathematical Society
• /
• v.26 no.3
• /
• pp.455-462
• /
• 2011

An analytic self-map ${\phi}$ of the open unit disk $\mathbb{D}$ in the complex plane and an analytic map ${\psi}$ on $\mathbb{D}$ induce the so-called weighted composition operator $C_{{\phi},{\psi}}$: $H(\mathbb{D})\;{\rightarrow}\;H(\mathbb{D})$, $f{\mapsto} \;{\psi}\;(f\;o\;{\phi})$, where H($\mathbb{D}$) denotes the set of all analytic functions on $\mathbb{D}$. We study when such an operator acting between different weighted Bergman spaces is bounded, compact and Schatten class.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.523-537
• /
• 2021

In this paper, we obtain some new inequalities for the Berezin number of operators on reproducing kernel Hilbert spaces by using the Hölder-McCarthy operator inequality. Also, we give refine generalized inequalities involving powers of the Berezin number for sums and products of operators on the reproducing kernel Hilbert spaces.