# Local entropy moduli and eigenvalues of operators in Banach spaces.

Revista Matemática Iberoamericana (1985)

- Volume: 1, Issue: 4, page 127-148
- ISSN: 0213-2230

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topCarl, Bernd, and Kühn, Thomas. "Local entropy moduli and eigenvalues of operators in Banach spaces.." Revista Matemática Iberoamericana 1.4 (1985): 127-148. <http://eudml.org/doc/39834>.

@article{Carl1985,

abstract = {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 between lp-spaces can be estimated. It is shown, that in general local and global degree of compactness considerably differ, but under certain type assumptions on the underlying Banach spaces they coincide. Finally, the results are applied to obtain (optimal) estimates for eigenvalues of certain integral operators.},

author = {Carl, Bernd, Kühn, Thomas},

journal = {Revista Matemática Iberoamericana},

keywords = {Espacios de Banach; Números de entropía; Operadores integrales; Problemas de autovalores; Operador absolutamente sumante; Local entropy moduli of bounded linear operators between Banach spaces; degree of compactness; s-numbers; eigenvalues; absolutely summing operators; inclusion; diagonal operators between -spaces; integral operators between -spaces},

language = {eng},

number = {4},

pages = {127-148},

title = {Local entropy moduli and eigenvalues of operators in Banach spaces.},

url = {http://eudml.org/doc/39834},

volume = {1},

year = {1985},

}

TY - JOUR

AU - Carl, Bernd

AU - Kühn, Thomas

TI - Local entropy moduli and eigenvalues of operators in Banach spaces.

JO - Revista Matemática Iberoamericana

PY - 1985

VL - 1

IS - 4

SP - 127

EP - 148

AB - 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 between lp-spaces can be estimated. It is shown, that in general local and global degree of compactness considerably differ, but under certain type assumptions on the underlying Banach spaces they coincide. Finally, the results are applied to obtain (optimal) estimates for eigenvalues of certain integral operators.

LA - eng

KW - Espacios de Banach; Números de entropía; Operadores integrales; Problemas de autovalores; Operador absolutamente sumante; Local entropy moduli of bounded linear operators between Banach spaces; degree of compactness; s-numbers; eigenvalues; absolutely summing operators; inclusion; diagonal operators between -spaces; integral operators between -spaces

UR - http://eudml.org/doc/39834

ER -

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