Arens simultaneously factorization

María José Aleandro

doi:10.2478/gm-2019-0002

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Arens simultaneously factorization

General Mathematics

Volume 27 (2019): Issue 1 (June 2019)

By: María José Aleandro

Open Access

|Dec 2019

Abstract

Let X be a Banach bimodule over a Banach algebra 𝒜. We shall seek conditions under which (1) X and its dual factorize on the same side or (2) X factors on the left (or right) if and only if its second conjugate space has a left (or right) unit.

References

[1] S. Ishikawa, Fixed point and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc., vol. 73, no. 2, 1976, 65-71.10.1090/S0002-9939-1976-0412909-X
Search in Google Scholar Back to article
[2] K. Haghnejad Azar, Arens regularity of bilinear forms and unital Banach module spaces, Bull. Iranian Math. Soc., vol. 40, no. 2, 2014, 505-520.
Search in Google Scholar Back to article
[3] P. Cohen, Factorization in group algebras, Duke Math. J., vol. 26, no. 2, 1959, 199-205.10.1215/S0012-7094-59-02620-1
Search in Google Scholar Back to article
[4] H. Dales , Banach algebras and automatic continuity, Oxford University Press, 2000.10.1093/oso/9780198500131.001.0001
Search in Google Scholar Back to article
[5] J. Dixmier, Les fonctionnelles linéaires sur l’ensemble des opérateurs bornées d’un espace de Hilbert, Ann. of Math., vol. 51, no. 2, 1950, 387-408.10.2307/1969331
Open DOI Search in Google Scholar Back to article
[6] N. Dunford, J. Schwartz, Linear operators I. General Theory, Interscience Publishers, 1958.
Search in Google Scholar Back to article
[7] E. Hewitt, K. Ross, Abstract harmonic analysis, Die Grundlehren der mathematischen Wissenschaften, 1963.
Search in Google Scholar Back to article
[8] A. Lau, A.Ülger, Topological centers of certain Banach algebras, Trans. Amer. Math. Soc., vol. 348, no. 3, 1996, 1191-1212.10.1090/S0002-9947-96-01499-7
Search in Google Scholar Back to article
[9] M. Leinert, A commutative Banach algebra which factorizes but has no approximate units, Proc. Amer. Math. Soc., vol. 55, no. 2, 1976, 245-246.10.1090/S0002-9939-1976-0397312-3
Search in Google Scholar Back to article
[10] W. Paschke, A factorable Banach algebra without bounded approximate unit, Pacific J. Math., vol. 46, no. 1, 1973, 249-251.10.2140/pjm.1973.46.249
Search in Google Scholar Back to article
[11] R. Schatten, A theory of cross-spaces, Princeton University Press, 1950.
Search in Google Scholar Back to article
[12] I. Segal, The group algebra of a locally compact group, Trans. Amer. Math. Soc., vol. 61, no. 1, 1947, 69-105.10.1090/S0002-9947-1947-0019617-4
Search in Google Scholar Back to article
[13] N. Young, Periodicity of functional and representations of normed algebras on reflexive spaces, Proc. Edinburgh Math. Soc., vol. 20, no. 2, 1976, 99-120.10.1017/S0013091500010610
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/gm-2019-0002 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

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Language: English

Page range: 17 - 27

Submitted on: Nov 14, 2018

Accepted on: Apr 29, 2019

Published on: Dec 21, 2019

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Related subjects:

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2019 María José Aleandro, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 27 (2019): Issue 1 (June 2019)