1973
DOI: 10.1090/s0002-9939-1973-0310685-x
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Representation theorems for compact operators

Abstract: It is shown that c0 (the Banach space of zeroconvergent sequences) is the only Banach space with basis that satisfies the following property: For every compact operator T:c"-->-E from c0 into a Banach space E, there is a sequence X in c0 and an unconditionally summable sequence {yn} in E such that Tn=J An/i"j" for each /i in c0. This result is then used to show that a linear operator T:E-*F from a locally convex space E into a Fréchet space Fhas a representation of the form Tx= y A"", where A is a seq… Show more

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Cited by 7 publications
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“…Another related representation theorem for compact maps emphasizing the factorization through c 0 can be found in [17]. Using all of the above results of Terzioğlu, the following conclusions are shown in [20].…”
Section: Definition 22mentioning
confidence: 84%
“…Another related representation theorem for compact maps emphasizing the factorization through c 0 can be found in [17]. Using all of the above results of Terzioğlu, the following conclusions are shown in [20].…”
Section: Definition 22mentioning
confidence: 84%