ScholarLens Back to search
2021•Kyushu Journal of MathematicsOpen access

ON THE SECOND DUAL SPACE OF THE BANACH SPACE OF VECTOR-VALUED LITTLE LIPSCHITZ FUNCTIONS

Shinnosuke Izumi

Open full text 0 citations

Abstract

Let X be a compact metric space and E be a Banach space. Then lip (X, E) denotes the Banach space of all E-valued little Lipschitz functions on X. We show that lip(X, E)∗∗ is isometrically isomorphic to the Banach space of E∗∗-valued Lipschitz functions Lip(X, E∗∗) under several conditions. Moreover, we describe the isometric isomorphism from lip(X, E)∗∗ to Lip(X, E∗∗).

Open-access reader

About this research paper

What this paper is about

Let X be a compact metric space and E be a Banach space. Then lip (X, E) denotes the Banach space of all E-valued little Lipschitz functions on X. We show that lip(X, E)∗∗ is isometrically isomorphic to the Banach space of E∗∗-valued Lipschitz functions Lip(X, E∗∗) under several conditions. Moreover, we describe the isometric isomorphism from lip(X, E)∗∗ to Lip(X, E∗∗).

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Let X be a compact metric space and E be a Banach space. Then lip (X, E) denotes the Banach space of all E-valued little Lipschitz functions on X. We show that lip(X, E)∗∗ is isometrically isomorphic to the Banach space of E∗∗-valued Lipschitz functions Lip(X, E∗∗) under several conditions. Moreover, we describe the isometric isomorphism from lip(X, E)∗∗ to Lip(X, E∗∗).

Key concepts: Mathematics, Lipschitz continuity, Banach space, Metric differential, Isomorphism (crystallography), Pure mathematics, Infinite-dimensional vector function, Space (punctuation)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
ON THE SECOND DUAL SPACE OF THE BANACH SPACE OF VECTOR-VALUED LITTLE LIPSCHITZ FUNCTIONS — Research Paper | ScholarLens