Search results for "Operator norm"

Dynamics of differentiation and integration operators on weighted spaces of entire functions

2014

Equivalences involving (p,q)-multi-norms

2014

Norm estimates for operators from Hp to ℓq

2008

Abstract We give upper and lower estimates of the norm of a bounded linear operator from the Hardy space H p to l q in terms of the norm of the rows and the columns of its associated matrix in certain vector-valued sequence spaces.

Essential norm estimates for composition operators on BMOA

2013

Abstract We provide two function-theoretic estimates for the essential norm of a composition operator C φ acting on the space BMOA; one in terms of the n-th power φ n of the symbol φ and one which involves the Nevanlinna counting function. We also show that if the symbol φ is univalent, then the essential norm of C φ is comparable to its essential norm on the Bloch space.

On norm attaining polynomials

2003

We show that for every Banach space X the set of 2-homogeneous continuous polynomials whose canonical extension to X∗∗ attain their norm is a dense subset of the space of all 2-homogeneous continuous polynomials P(2X).

On the operators which are invertible modulo an operator ideal

2001

Atkinson [3] studied the operators which are left invertible $i(X, Y) or right invertible $T{X, Y) modulo /C, with K. the compact operators. He proved that an operator T € C(X, Y) belongs to <£/ or $ r if and only if the kernel and the range of T are complemented and additionally, the kernel is finite dimensional or the range is finite codimensional, respectively. Yood [19] obtained some perturbation results for these classes and Lebow and Schechter [12] proved that the inessential operators form the perturbation class for $,(A") and $r{X). Yang [18] extended some results of ^3, 19] to operators invertible modulo W, with W the weakly compact operators. His aim was to study a generalised Fre…

Property (R) for Bounded Linear Operators

2011

We introduce the spectral property (R), for bounded linear operators defined on a Banach space, which is related to Weyl type theorems. This property is also studied in the framework of polaroid, or left polaroid, operators.

Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets

2006

Let A be a uniform algebra, and let o be a self-map of the spectrum M A of A that induces a composition operator C o on A. The object of this paper is to relate the notion of "hyperbolic boundedness" introduced by the authors in 2004 to the essential spectrum of C o . It is shown that the essential spectral radius of C o , is strictly less than 1 if and only if the image of M A under some iterate o n of o is hyperbolically bounded. The set of composition operators is partitioned into "hyperbolic vicinities" that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm.

Ergodic properties of operators in some semi-Hilbertian spaces

2012

This article deals with linear operators T on a complex Hilbert space ℋ, which are bounded with respect to the seminorm induced by a positive operator A on ℋ. The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesaro ergodic, such that T  * is not a quasiaff…

Metric operators, generalized hermiticity and partial inner product spaces

2015

A quasi-Hermitian operator is an operator in a Hilbert space that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure of metric operators, bounded or unbounded, in a Hilbert space. We introduce several generalizations of the notion of similarity between operators and explore to what extent they preserve spectral properties. Next we consider canonical lattices of Hilbert spaces generated by unbounded metric operators. Since such lattices constitute the simplest case of a partial inner product space (PIP space), we can exploit the te…