2022
DOI: 10.52968/28305203
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Approximate Identities in Algebras of Compact Operators on Frechet Spaces

Abstract: Bounded approximate identity(bai) is a key concept in the theory of amenability of algebras. In this paper, we show that algebra of compact operators on Frechet space X has both the right and left locally bounded approximate identities. Sufficient conditions for the existence of these identities are established based on the geometry properties of the Frechet space X and its dual space X' respectively.

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“…Its notions therefore generalize Banach space and Hilbert spaces. Any algebra A equipped with a structure of lcs with respect to which the product is separately continuous is a topological algebra [3]. So, a Frechet algebra is a complete topological algebra of which an increasing countable collection {pi; i ∈ N} of sub-multiplicative continuous semi-norms determines its topology.…”
Section: Frechet Space Of Operator Idealsmentioning
confidence: 99%
“…Its notions therefore generalize Banach space and Hilbert spaces. Any algebra A equipped with a structure of lcs with respect to which the product is separately continuous is a topological algebra [3]. So, a Frechet algebra is a complete topological algebra of which an increasing countable collection {pi; i ∈ N} of sub-multiplicative continuous semi-norms determines its topology.…”
Section: Frechet Space Of Operator Idealsmentioning
confidence: 99%