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Mathematics 2019, 7(4), 347; https://doi.org/10.3390/math7040347

Structure of Normed Simple Annihilator Algebras

Department of Appl. Mathematics, Moscow State Techn. Univ. MIREA, av. Vernadksy 78, Moscow 119454, Russia
Received: 18 February 2019 / Revised: 29 March 2019 / Accepted: 2 April 2019 / Published: 11 April 2019
PDF [245 KB, uploaded 11 April 2019]

Abstract

This article is devoted to normed simple annihilator algebras. Their structure is investigated in the paper. Maximal families of orthogonal irreducible idempotents of normed simple annihilator algebras are scrutinized. Division subalgebras of annihilator algebras are studied. Realizations of these algebras by operator algebras in Banach spaces are described. For this purpose, quasi finite dimensional operators are investigated.
Keywords: operator; algebra; norm; ideal; annihilator; infinite dimension; field operator; algebra; norm; ideal; annihilator; infinite dimension; field
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ludkowski, S.V. Structure of Normed Simple Annihilator Algebras. Mathematics 2019, 7, 347.

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