## Algebras for matrix limitation

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1977##### Permanent Link

http://hdl.handle.net/10092/11599Let A= (a m,n) be a regular matrix; by A is denoted the set of sequences limited by A and by A₀ those sequences limited to zero by A. If 𝜉 = { 𝜉n } is a bounded sequence and { 𝜉n sn } ∈ A₀ whenever {sn} ∈ A₀ then 𝜉 is called an f-sequence for the matrix A= (a m,n ). The set of f-sequences form an algebra denoted by A⁰. By A(A₀) are denoted those bounded sequences limited (to zero) by A and by A⁰ the algebra of bounded sequences 𝜉, such that 𝜉, x ∈ A₀ whenever x ∈ A₀. It is easy to prove that A⁰ is a Banach Algebra. The sequences of A⁰ and A⁰ have been used by many authors, notably by Agnew, [1], Brudno [3], Bosanquet [6], Erdos and Piranian [ 7] and Zeller [20]. Goes [ 8] took up the study of Banach Algebras of bounded sequences in general.

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Field of Research::01 - Mathematical Sciences::0101 - Pure Mathematics::010108 - Operator Algebras and Functional Analysis##### Collections

- Engineering: Reports [693]