# On the structure of tensor norms related to (p,σ)-absolutely continuous operators.

Collectanea Mathematica (1996)

- Volume: 47, Issue: 1, page 35-46
- ISSN: 0010-0757

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topSánchez-Pérez, Enrique A.. "On the structure of tensor norms related to (p,σ)-absolutely continuous operators.." Collectanea Mathematica 47.1 (1996): 35-46. <http://eudml.org/doc/40195>.

@article{Sánchez1996,

abstract = {We define an interpolation norm on tensor products of p-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm. We obtain substitutes of the Chevet-Persson-Saphar inequalities for this case. We also use the calculus of traced tensor norms in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of (p, sigma)-absolutely continuous operators defined by Jarchow and Matter. As an application we find the largest tensor norm less than or equal to our interpolation norm.},

author = {Sánchez-Pérez, Enrique A.},

journal = {Collectanea Mathematica},

keywords = {Operador absolutamente continuo; Análisis tensorial; Espacios normados; Espacios de funciones; Espacios de Banach; Integrabilidad; absolutely summing operators; interpolation norm; tensor products of -integrable function spaces; Bochner norm; injective norm; Chevet-Persson-Saphar inequalities; interpolated ideal of -absolutely continuous operators; ideal of -summing operators},

language = {eng},

number = {1},

pages = {35-46},

title = {On the structure of tensor norms related to (p,σ)-absolutely continuous operators.},

url = {http://eudml.org/doc/40195},

volume = {47},

year = {1996},

}

TY - JOUR

AU - Sánchez-Pérez, Enrique A.

TI - On the structure of tensor norms related to (p,σ)-absolutely continuous operators.

JO - Collectanea Mathematica

PY - 1996

VL - 47

IS - 1

SP - 35

EP - 46

AB - We define an interpolation norm on tensor products of p-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm. We obtain substitutes of the Chevet-Persson-Saphar inequalities for this case. We also use the calculus of traced tensor norms in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of (p, sigma)-absolutely continuous operators defined by Jarchow and Matter. As an application we find the largest tensor norm less than or equal to our interpolation norm.

LA - eng

KW - Operador absolutamente continuo; Análisis tensorial; Espacios normados; Espacios de funciones; Espacios de Banach; Integrabilidad; absolutely summing operators; interpolation norm; tensor products of -integrable function spaces; Bochner norm; injective norm; Chevet-Persson-Saphar inequalities; interpolated ideal of -absolutely continuous operators; ideal of -summing operators

UR - http://eudml.org/doc/40195

ER -

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