On state space of measurable function in symmetric Δ-Banach algebra with new results

The aim of this paper is to present new results obtained in the study of spaces with a Δ-symmetric Banach Algebra, we defined the δ-characters functional and discuss the space of measurable function(Lo(µ)) is Δ- symmetric and is Banach algebra. Also, we define sℂ(Lo(µ)) by depended on Lo(µ) and prov...

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Bibliographic Details
Published in:AIP conference proceedings 2022-10, Vol.2398 (1)
Main Authors: Hussein, Boushra Y., Wshayeh, Huda A. A.
Format: Article
Language:English
Subjects:
Algebra
Banach spaces
Continuity (mathematics)
Online Access:Get full text
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Summary:The aim of this paper is to present new results obtained in the study of spaces with a Δ-symmetric Banach Algebra, we defined the δ-characters functional and discuss the space of measurable function(Lo(µ)) is Δ- symmetric and is Banach algebra. Also, we define sℂ(Lo(µ)) by depended on Lo(µ) and proved the spaces is satisfies new properties in symmetric Banach algebra and prove any function in sℂ(Lo(µ)) satisfies all conditions of state functional and found corresponding between the space sℂ(Lo(µ)) and the space of all o- characters functional δch(Lo(µ)) on Lo(µ) as well as well defined. Also, we proved the functional ψ from Æ into sℂ(Lo(µ)) is continuous and state functional if every non-zero element has an inverse. We proved the quotient sℂ(Lo(µ))/Ι is also symmetric Δ –Banach algebra.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0093486