WebJul 16, 2012 · It is shown that every weakly $p$-summable sequence in $X$ is operator $p$-summable if and only if every operator $T \in B(X, l_p)$ is $p$-absolutely summing. … WebJan 1, 1993 · A sequence (x n ) in X is called weakly p-convergent to x ∈ X if the sequence (x n − x) is weakly p-summable [6]. Weakly ∞-convergent sequences are precisely the …

real analysis - Proving $f_n$ is weakly convergent to $f$ if …

WebThe sequence ( xn) is weakly p-summuble if for each x * ∈ X * this linear space of X -valued sequences is a Banach space (if X is) when the ℓ pweak -norm The sequence ( yn) in Y is the absolutely p -summable when naturally, is just . Again, is a Banach space (if Y is). WebJul 7, 2016 · • A subset K of a Banach space X is called weakly p-precompact, if every sequence from K has a weakly p-Cauchy subsequence. The weakly ∞-precompact sets are precisely the weakly... raw shrimp in air fryer recipe

reference request - Does taking the modulus preserve weak $p ...

Web2 HENRIK WIRZENIUS The main purpose of the present paper is to establish new results on the Kup-AP in the case of 1 ≤ p < 2.We approach the Kup-AP mainly through the characterisation Kup = Ksur p′ due to Muñoz et al. [31] (also Fourie [14]), where Ksur p′ denotes the surjective hull of the Banach operator ideal Kp′ of the (classical) p′-compact … WebFeb 3, 2016 · A sequence $(x_n)$ is weakly $p$ summable if the mapping $e_n\mapsto x_n$ extends to a bounded linear operator from $\ell_{p^*}$ into $X$. IMO, this is the … WebAug 13, 2013 · A sequence 〈 xn 〉 in a Banach space X is defined to be p -operator summable if for each 〈 fn 〉 ∈ lw*p(X*) we have 〈〈 fn(xk) 〉 k 〉 n ∈ lsp(lp). Every … raw shrimp in refrigerator how long