The closeness of almost multiplicative linear functionals with multiplicative linear functionals in commutative Banach algebras

Subject Areas : Statistics

ّّFariba  Ershad ¹ (Department of Mathematics, Payame Noor University, Iran)

Received: 2019-01-28 Accepted : 2020-01-18 Published : 2021-02-19

Keywords: تابعک خطی ضربی, حاصلضرب دکارتی, فضای دنباله‌ای, جبرهای باناخ, تابعک تقریبا خطی ضربی,

Abstract :

In this paper we will give the definition of almost multiplicative linear functionals on commutative Banach algebras and investigate the closeness of these linear functionals with multiplicative linear functionals (AMNM property) . َSeveral Banach algebra has this property, but not all of them. Due to relationship between the spectrum of an element of a complex Banach algebra and multiplicative linear functionals. Thus this investigation about almost multiplicative linear functionals give us some information about the spectrum of an element of a Banach algebra. In this paper We will give a very helpful theorem, for this investigation. Also we will show that, if in two commutative Banach algebras A and B, near any almost multiplicative linear functional, there is a multiplicative linear functional, then A×B also has this property and vice versa. We investigate this property for finite product of commutative Banach algebras. Also we will refer to some of the sequential spaces.

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