On one class of matrix differential operators.
On one class of operators associated with differential equations of fractional order.
On one subset M. Schechter's essential spectrum
On operator bands
A multiplicative semigroup of idempotent operators is called an operator band. We prove that for each K>1 there exists an irreducible operator band on the Hilbert space which is norm-bounded by K. This implies that there exists an irreducible operator band on a Banach space such that each member has operator norm equal to 1. Given a positive integer r, we introduce a notion of weak r-transitivity of a set of bounded operators on a Banach space. We construct an operator band on that is weakly...
On operator ideals determined by sequences.
On operator valued solutions of d'Alembert's functional equation, II
On operators Cauchy dual to 2-hyperexpansive operators: the unbounded case
The Cauchy dual operator T’, given by , provides a bounded unitary invariant for a closed left-invertible T. Hence, in some special cases, problems in the theory of unbounded Hilbert space operators can be related to similar problems in the theory of bounded Hilbert space operators. In particular, for a closed expansive T with finite-dimensional cokernel, it is shown that T admits the Cowen-Douglas decomposition if and only if T’ admits the Wold-type decomposition (see Definitions 1.1 and 1.2 below)....
On operators close to isometries
We introduce and discuss a class of operators, to be referred to as operators close to isometries. The Bergman-type operators, 2-hyperexpansions, expansive p-isometries, and certain alternating hyperexpansions are main examples of such operators. We establish a few decomposition theorems for operators close to isometries. Applications are given to the theory of p-isometries and of hyperexpansive operators.
On operators factorizable through space
On operators fixing copies of and
On Operators in Bochner Spaces
On operators induced by weakly 2-singular kernels
On operators of Saphar type.
On operators on
On operators T such that f(T) is hypercyclic
On operators T such that f(T) is hypercyclic.
On operators T such that Weyl's theorem holds for f(T).
On Operators with Bounded Imaginary Powers in Banach Spaces.
On operators with the same local spectra
Let be the algebra of all bounded linear operators in a complex Banach space . We consider operators satisfying the relation for any vector , where denotes the local spectrum of at the point . We say then that and have the same local spectra. We prove that then, under some conditions, is a quasinilpotent operator, that is as . Without these conditions, we describe the operators with the same local spectra only in some particular cases.
On operators with the same spectrum