Isometries of certain operator spaces

R. Khalil; A. Saleh

doi:10.1090/S0002-9939-03-07210-1

Isometries of certain operator spaces

R. Khalil, A. Saleh

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let X and Y be Banach spaces, and L(X, Y) be the spaces of bounded linear operators from X into Y. In this paper we give full characterization of isometric onto operators of L(X, Y), for a certain class of Banach spaces, that includes ℓ^p, 1 < p < ∞. We also characterize the isometric onto operators of L(c₀) and K(ℓ¹), the compact operators on ℓ¹. Furthermore, the multiplicative isometric onto operators of L(ℓ¹), when multiplication on L(ℓ¹) is taken to be the Schur product, are characterized.

Original language	English
Pages (from-to)	1473-1481
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	132
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9939-03-07210-1
State	Published - May 2004
Externally published	Yes

Keywords

Isometries
Operator spaces

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10.1090/S0002-9939-03-07210-1

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AB - Let X and Y be Banach spaces, and L(X, Y) be the spaces of bounded linear operators from X into Y. In this paper we give full characterization of isometric onto operators of L(X, Y), for a certain class of Banach spaces, that includes ℓp, 1 < p < ∞. We also characterize the isometric onto operators of L(c0) and K(ℓ1), the compact operators on ℓ1. Furthermore, the multiplicative isometric onto operators of L(ℓ1), when multiplication on L(ℓ1) is taken to be the Schur product, are characterized.

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KW - Operator spaces

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

Isometries of certain operator spaces

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Keywords

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