Composition, numerical range and aron-berner extension

Yun Sung Choi; Domingo García; Sung Guen Kim; Manuel Maestre

doi:10.7146/math.scand.a-15071

Composition, numerical range and aron-berner extension

Yun Sung Choi, Domingo García, Sung Guen Kim, Manuel Maestre

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

17 Scopus citations

Abstract

Given an entire mapping f ∈ ℋ_b(X, X) of bounded type from a Banach space X into X, we denote by f̄ the Aron-Berner extension of f to the bidual X** of X. We show that ḡ ō f̄ = ḡ o f̄ for all f, g ∈ ℋb(X, X) if X is symmetrically regular. We also give a counterexample on li such that the equality does not hold. We prove that the closure of the numerical range of f is the same as that of f̄.

Original language	English
Pages (from-to)	97-110
Number of pages	14
Journal	Mathematica Scandinavica
Volume	103
Issue number	1
DOIs	https://doi.org/10.7146/math.scand.a-15071
State	Published - 2008

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AU - Choi, Yun Sung

AU - García, Domingo

AU - Kim, Sung Guen

AU - Maestre, Manuel

PY - 2008

Y1 - 2008

N2 - Given an entire mapping f ∈ ℋb(X, X) of bounded type from a Banach space X into X, we denote by f̄ the Aron-Berner extension of f to the bidual X** of X. We show that ḡ ō f̄ = ḡ o f̄ for all f, g ∈ ℋb(X, X) if X is symmetrically regular. We also give a counterexample on li such that the equality does not hold. We prove that the closure of the numerical range of f is the same as that of f̄.

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UR - https://www.scopus.com/pages/publications/54949120277

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Composition, numerical range and aron-berner extension

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