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On strong M-bases in Banach spaces with PRI.

Deba P. Sinha (2000)

Collectanea Mathematica

If every member of a class P of Banach spaces has a projectional resolution of the identity such that certain subspaces arising out of this resolution are also in the class P, then it is proved that every Banach space in P has a strong M-basis. Consequently, every weakly countably determined space, the dual of every Asplund space, every Banach space with an M-basis such that the dual unit ball is weak* angelic and every C(K) space for a Valdivia compact set K , has a strong M-basis.

On strongly l p -summing m-linear operators

Lahcène Mezrag (2008)

Colloquium Mathematicae

We introduce and study a new concept of strongly l p -summing m-linear operators in the category of operator spaces. We give some characterizations of this notion such as the Pietsch domination theorem and we show that an m-linear operator is strongly l p -summing if and only if its adjoint is l p -summing.

On strongly Pettis integrable functions in locally convex spaces.

N. D. Chakraborty, Sk. Jaker Ali (1993)

Revista Matemática de la Universidad Complutense de Madrid

Some characterizations have been given for the relative compactness of the range of the indefinite Pettis integral of a function on a complete finite measure space with values in a quasicomplete Hausdorff locally convex space. It has been shown that the indefinite Pettis integral has a relatively compact range if the functions is measurable by seminorm. Separation property has been defined for a scalarly measurable function and it has been proved that a function with this property is integrable...

On subrelations of ergodic measured type III equivalence relations

Alexandre Danilenko (2000)

Colloquium Mathematicae

We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.

On subspaces of Banach spaces where every functional has a unique norm-preserving extension

Eve Oja, Märt Põldvere (1996)

Studia Mathematica

Let X be a Banach space and Y a closed subspace. We obtain simple geometric characterizations of Phelps' property U for Y in X (that every continuous linear functional g ∈ Y* has a unique norm-preserving extension f ∈ X*), which do not use the dual space X*. This enables us to give an intrinsic geometric characterization of preduals of strictly convex spaces close to the Beauzamy-Maurey-Lima-Uttersrud criterion of smoothness. This also enables us to prove that the U-property of the subspace K(E,F)...

Currently displaying 1001 – 1020 of 1948