All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 10 Next

Displaying 181 – 200 of 501

Showing per page

Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces

Bernd Carl (1985)

Annales de l'institut Fourier

The paper deals with covering problems and the degree of compactness of operators. The main part is devoted to relationships between entropy moduli and Kolmogorov (resp. Gelfand and approximation) numbers for operators which may be interpreted as counterparts to the classical Bernstein-Jackson inequalities for functions. Certain quantifications of results in the Riesz-Schauder-Theory are given. Finally, the largest distance between “the degree of approximation” and the “degree of compactness” of...

Isolated points of spectrum of k-quasi-*-class A operators

Salah Mecheri (2012)

Studia Mathematica

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class, denoted *, of operators satisfying T * k ( | T ² | - | T * | ² ) T k ≥ 0 where k is a natural number, and we prove basic structural properties of these operators. Using these results, we also show that if E is the Riesz idempotent for a non-zero isolated point μ of the spectrum of T ∈ *, then E is self-adjoint and EH = ker(T-μ) = ker(T-μ)*. Some spectral properties are also presented.

Lineability of functionals and operators

Francisco Javier García-Pacheco, Daniele Puglisi (2010)

Studia Mathematica

This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show that the...

Little G. T. for lp-lattice summing operators

Mezrag, Lahcène (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B28, 47D15.In this paper we introduce and study the lp-lattice summing operators in the category of operator spaces which are the analogous of p-lattice summing operators in the commutative case. We study some interesting characterizations of this type of operators which generalize the results of Nielsen and Szulga and we show that Λ l∞( B(H) ,OH) ≠ Λ l2( B( H) ,OH), in opposition to the commutative case.

Local entropy moduli and eigenvalues of operators in Banach spaces.

Bernd Carl, Thomas Kühn (1985)

Revista Matemática Iberoamericana

In the paper local entropy moduli of operators between Banach spaces are introduced. They constitue a generalization of entropy numbers and moduli, and localize these notions in an appropriate way. Many results regarding entropy numbers and moduli can be carried over to local entropy moduli. We investigate relations between local entropy moduli and s-numbers, spectral properties, eigenvalues, absolutely summing operators. As applications, local entropy moduli of identical and diagonal operators...

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Krzysztof Nowak (1996)

Studia Mathematica

We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions g ↦ P g , ϕ , where for a fixed function ϕ, P g , ϕ denotes the one-dimensional orthogonal projection on the function U g ϕ , U is a group representation and g is an element of the group. They are defined as integrals ʃ W P g , ϕ d g , where W is an open, relatively...

Log-majorizations and norm inequalities for exponential operators

Fumio Hiai (1997)

Banach Center Publications

Concise but self-contained reviews are given on theories of majorization and symmetrically normed ideals, including the proofs of the Lidskii-Wielandt and the Gelfand-Naimark theorems. Based on these reviews, we discuss logarithmic majorizations and norm inequalities of Golden-Thompson type and its complementary type for exponential operators on a Hilbert space. Furthermore, we obtain norm convergences for the exponential product formula as well as for that involving operator means.

Currently displaying 181 – 200 of 501