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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 polynomials are polynomials

C. Fong, G. Lumer, E. Nordgren, H. Radjavi, P. Rosenthal (1995)

Studia Mathematica

We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.

Local properties of accessible injective operator ideals

F. Oertel (1998)

Czechoslovak Mathematical Journal

In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a “good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessibility condition (theorem 3.1). This observation leads in a natural way to a characterization of accessible...

Local spectrum and local spectral radius of an operator at a fixed vector

Janko Bračič, Vladimír Müller (2009)

Studia Mathematica

Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() with σ T ( e ) = σ δ ( T ) , respectively r T ( e ) = r ( T ) , is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.

Locally spectrally bounded linear maps

M. Bendaoud, M. Sarih (2011)

Mathematica Bohemica

Let ℒ ( ℋ ) be the algebra of all bounded linear operators on a complex Hilbert space ℋ . We characterize locally spectrally bounded linear maps from ℒ ( ℋ ) onto itself. As a consequence, we describe linear maps from ℒ ( ℋ ) onto itself that compress the local spectrum.

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 41 – 60 of 66