Completion problems for operator matrices are concerned with the question of whether a
partially specified operator matrix can be completed to form an operator of a desired type …

Let T and S be Hilbert space operators such that Weyl's theorem holds for both of them. In
general, it does not follow that Weyl's theorem holds for the direct sum T⊕ S. We give …

For a Banach space operator T∈ B (X), it is proved that if either T is an algebraically, totally
hereditarily normaloid operator and the Banach space X is separable, or T satisfies the …

An operator T belonging to the algebra B (H) of bound-ed linear transformations on a Hilbert
H into itself is said to be posinormal if there exists a positive operator PGB (H) such that TT" …

For a bounded operator T acting on an infinite dimensional separable Hilbert space H, we
prove the following assertions:(i) If T or T*∈, then generalized a-Browder's theorem holds for …

SVEP and Generalized Weyl’s Theorem Page 1 Mediterr. j. math. 4 (2007), 309–320 1660-5446/030309-12,
DOI 10.1007/s00009-007-0120-3 c© 2007 Birkhäuser Verlag Basel/Switzerland …

In this paper we consider the problem of completion of the upper-triangular operator matrix
[A? 0 B] where A∈ B (H) and B∈ B (K), to Kato nonsingular operators and completely solve …

A Banach space operator $ T $ is completely hereditarily normaloid, $ T\in\mathcal {CHN} $,
if either every part, and (also) $ T_p^{-1} $ for every invertible part $ T_p $, of $ T $ is …

A Banach space operator Τ∊ 𝙱 (𝒳) satisfies a local growth condition of order 𝓂 for some
positive integer 𝓂, Τ∊ loc (Gₘ), if for every closed subset 𝐹 of the set of complex numbers …

It is known that if A ∈ B\left (V\right) and B ∈ B\left (W\right) are Banach space operators
with the single-valued extension property, SVEP, then the matrix operator M_C=\left () has …