1979
DOI: 10.1007/bf01170259
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Banach ideals of p-compact operators

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1981
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Cited by 35 publications
(30 citation statements)
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“…The space pu(X) is defined as the (closed) subspace of pw(X), formed by the (xn)pw(X) satisfying (xn)=trueprefixlimN(x1,,xN,0,0,) in pw(X). The space pu(X) was introduced and thoroughly studied by Fourie and Swart in 1979. In particular, it follows from [, Theorem 1.4] that Φ(xn) is compact whenever (xn)pu(X).…”
Section: Unconditionally and Weakly (Pr)‐null Sequencesmentioning
confidence: 99%
See 3 more Smart Citations
“…The space pu(X) is defined as the (closed) subspace of pw(X), formed by the (xn)pw(X) satisfying (xn)=trueprefixlimN(x1,,xN,0,0,) in pw(X). The space pu(X) was introduced and thoroughly studied by Fourie and Swart in 1979. In particular, it follows from [, Theorem 1.4] that Φ(xn) is compact whenever (xn)pu(X).…”
Section: Unconditionally and Weakly (Pr)‐null Sequencesmentioning
confidence: 99%
“…The space pu(X) was introduced and thoroughly studied by Fourie and Swart in 1979. In particular, it follows from [, Theorem 1.4] that Φ(xn) is compact whenever (xn)pu(X). In fact, Φ(xn):p*X is compact if and only if (xn)pu(X) (see [, Theorem 1.4] or, e.g., [, 8.2]).…”
Section: Unconditionally and Weakly (Pr)‐null Sequencesmentioning
confidence: 99%
See 2 more Smart Citations
“…The link between these notions of nullity and null sequences given by operator ideals is as follows: p ‐null sequences correspond with Np‐null sequences with Np the ideal of right p ‐nuclear operators [, Proposition 1.4 and Remark 1.3]. Also, unconditionally p ‐null sequences coincides with Kp‐null sequences [, Corollary 4.2], where Kp is the ideal of the classical p‐compact operators of Fourie and Swart and p is the conjugate of p . Taking this into account, the results by Oja and Kim read as follows: c0,scriptNpfalse(Xfalse)=c0truêdpX and c0,frakturKpfalse(Xfalse)=c0truêwpX, respectively.…”
Section: Introductionmentioning
confidence: 99%