• East Asian mathematical journal
• /
• 제14권1호
• /
• pp.21-26
• /
• 1998

The Fulgede-Putnam theorem asserts as if A and Bare normal operators and X is an operator such that AX=XB, then A*X=XB*. In this paper, we show that if A is k-quasihyponormal and B* is invertible k-quasihyponormal such that AX=XB for a Hilbert-Schmidt operator X, then A*X=XB*.

• 대한수학회보
• /
• 제29권2호
• /
• pp.295-300
• /
• 1992

In [5] it was shown that if T .mem. L(X) is regular on a Banach space X, with finite dimensional intersection T$^{-1}$ (0).cap.T(X) and if S .mem. L(X) is invertible, commute with T and has sufficiently small norm then T - S in upper semi-Fredholm, and hence essentially one-one, in the sense that the null space of T - S is finite dimensional ([4] Theorem 2; [5] Theorem 2). In this note we extend this result to incomplete normed space.

• 대한수학회보
• /
• 제40권1호
• /
• pp.53-61
• /
• 2003

We prove the generalized Hyers-Ulam-Rassias stability of the invertible mapping in a Banach module over a unital Banach algebra, and prove the generalized Hyers-Ulam-Rassias stability of the Jensen's functional equations in a Hilbert module over a unital $C^{*}$-algebra.

• 대한수학회보
• /
• 제28권2호
• /
• pp.185-190
• /
• 1991

The concept of "almost invertibility modulo closed ideals" in L(X, Y) was introduced, implicitly, by Robin Harte [1, Theorem 3.9.5]. The aims of this note are to make the formal definition of "almost left and right invertible modulo closed ideals" operators and show that they form open sets.they form open sets.

• 대한수학회지
• /
• 제51권2호
• /
• pp.363-382
• /
• 2014

In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces $L^2(\mathbb{N},\mathcal{K})$ (or $L^2(\mathbb{Z},\mathcal{K})$) with weight sequence {$A_n$} of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$. Then we give the necessary and sufficient conditions for the supercyclicity of those weighted shifts, which extends some previous results of H. Salas. At last, we give some conditions for the supercyclicity of three different weighted shifts.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제25권1호
• /
• pp.39-48
• /
• 2018

In this work, by applying the binomial expansion, some refinements of the Young and Heinz inequalities are proved. As an application, a determinant inequality for positive definite matrices is obtained. Also, some operator inequalities around the Young's inequality for semidefinite invertible matrices are proved.

• Kyungpook Mathematical Journal
• /
• 제58권3호
• /
• pp.463-472
• /
• 2018

A Q-module is a module in which every nonzero submodule of M is a finite product of primary submodules of M. This paper is devoted to study some properties of Dedekind modules and Q-modules.

• 대한수학회지
• /
• 제44권4호
• /
• pp.903-913
• /
• 2007

A ring R has weakly stable range one provided that aR+bR=R implies that there exists a $y{\in}R$ such that $a+by{\in}R$ is right or left invertible. We prove, in this paper, that every regular element in an exchange ring having weakly stable range one is the sum of an idempotent and a weak unit. This generalize the corresponding result of one-sided unit-regular ring. Extensions of power comparability and power cancellation are also studied.

• Korean Journal of Mathematics
• /
• 제29권3호
• /
• pp.511-518
• /
• 2021

In this paper, a relationship between the extended spectrum of the Aluthge transform and the extended spectrum of the operator T is proved. Other relationships between two different operators and other results are also given.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.705-718
• /
• 2022

In this paper, for bounded linear operators A, B, C satisfying [AB, B] = [BC, B] = [AB, BC] = 0 we study the Drazin invertibility of the sum of products formed by the three operators A, B and C. In particular, we give an explicit representation of the anti-commutator {A, B} = AB + BA. Also we give some conditions for which the sum A + C is Drazin invertible.