Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_p$-spaces

Oleg Reinov; Qaisar Latif

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Displaying similar documents to “Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_{p}$ -spaces”

The classical subspaces of the projective tensor products of $ℓ_{p}$ and C(α) spaces, α < ω₁

Elói Medina Galego, Christian Samuel (2013)

Studia Mathematica

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We completely determine the $ℓ_{q}$ and C(K) spaces which are isomorphic to a subspace of $ℓ_{p} \otimes ̂_{π} C (α)$ , the projective tensor product of the classical $ℓ_{p}$ space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from $ℓ_{p}$ to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states...

Nevanlinna algebras

A. Haldimann, H. Jarchow (2001)

Studia Mathematica

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The Nevanlinna algebras, $_{α}^{p}$ , of this paper are the $L^{p}$ variants of classical weighted area Nevanlinna classes of analytic functions on = z ∈ ℂ: |z| < 1. They are F-algebras, neither locally bounded nor locally convex, with a rich duality structure. For s = (α+2)/p, the algebra $F_{s}$ of analytic functions f: → ℂ such that ${(1 - | z |)}^{s} | f (z) | \to 0$ as |z| → 1 is the Fréchet envelope of $_{α}^{p}$ . The corresponding algebra $_{s}^{\infty}$ of analytic f: → ℂ such that $s u p_{z \in} {(1 - | z |)}^{s} | f (z) | < \infty$ is a complete metric space but fails to be a topological vector space....

2-summing multiplication operators

Dumitru Popa (2013)

Studia Mathematica

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Let 1 ≤ p < ∞, $= {(X ₙ)}_{n \in ℕ}$ be a sequence of Banach spaces and $l_{p} ()$ the coresponding vector valued sequence space. Let $= {(X ₙ)}_{n \in ℕ}$ , $= {(Y ₙ)}_{n \in ℕ}$ be two sequences of Banach spaces, $= {(V ₙ)}_{n \in ℕ}$ , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator $M_{} : l_{p} () \to l_{q} ()$ by $M_{} ({(x ₙ)}_{n \in ℕ}) : = {(V ₙ (x ₙ))}_{n \in ℕ}$ . We give necessary and sufficient conditions for $M_{}$ to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞. ...

The ideal of p-compact operators: a tensor product approach

Daniel Galicer, Silvia Lassalle, Pablo Turco (2012)

Studia Mathematica

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We study the space of p-compact operators, $_{p}$ , using the theory of tensor norms and operator ideals. We prove that $_{p}$ is associated to $/ d_{p}$ , the left injective associate of the Chevet-Saphar tensor norm $d_{p}$ (which is equal to $g_{p^{'}}^{'}$ ). This allows us to relate the theory of p-summing operators to that of p-compact operators. Using the results known for the former class and appropriate hypotheses on E and F we prove that $_{p} (E; F)$ is equal to $_{q} (E; F)$ for a wide range of values of p and q, and show that our results...