Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On operators from $ℓ_{s}$ to $ℓ_{p} ⊗̂ ℓ_{q}$ or to $ℓ_{p} \widehat{⊗̂} ℓ_{q}$

100%

Samuel C.

Colloquium Mathematicum

2010

tom 121

nr 1

25-33

We show that every operator from $ℓ_{s}$ to $ℓ_{p} ⊗̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \widehat{⊗̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

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

63%

Galego E., Samuel C.

Studia Mathematica

2013

tom 214

nr 3

237-250

We completely determine the $ℓ_{q}$ and C(K) spaces which are isomorphic to a subspace of $ℓ_{p} ⊗̂_{π} C(α)$, 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 that the only $ℓ_{q}$ space which is isomorphic to a subspace of $ℓ_{p} ⊗̂_{π} C(α)$ with 1 ≤ p ≤ q < ∞ and ω ≤ α < ω₁ is $ℓ_{p}$. The second main theorem concerning C(K) spaces improves a result of Bessaga and Pełczyński which allows us to classify, up to isomorphism, the separable spaces 𝓝(X,Y) of nuclear operators, where X and Y are direct sums of $ℓ_{p}$ and C(K) spaces. More precisely, we prove the following cancellation law for separable Banach spaces. Suppose that K₁ and K₃ are finite or countable compact metric spaces of the same cardinality and 1 < p, q < ∞. Then, for any infinite compact metric spaces K₂ and K₄, the following statements are equivalent: (a) $𝓝(ℓ_{p}⊕ C(K₁),ℓ_{q}⊕ C(K₂))$ and $𝓝(ℓ_{p}⊕ C(K₃),ℓ_{q}⊕ C(K₄))$ are isomorphic. (b) C(K₂) is isomorphic to C(K₄).

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Samuel C.

1 Galego E.

1 2013

1 2010

Wyniki wyszukiwania

On operators from $ℓ_{s}$ to $ℓ_{p} ⊗̂ ℓ_{q}$ or to $ℓ_{p} \widehat{⊗̂} ℓ_{q}$

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