All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 114 Next

Displaying 2261 – 2280 of 3166

Showing per page

Rich families and elementary submodels

Marek Cúth, Ondřej Kalenda (2014)

Open Mathematics

We compare two methods of proving separable reduction theorems in functional analysis - the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality...

Rosenthal operator spaces

M. Junge, N. J. Nielsen, T. Oikhberg (2008)

Studia Mathematica

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an L p -space, then it is either an L p -space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non-Hilbertian complemented operator subspaces of non-commutative L p -spaces and show that this class is much richer than in the commutative case. We investigate the local properties of some new classes of operator spaces for every 2 < p < ∞ which can be considered...

Rotund and uniformly rotund Banach spaces.

V. Montesinos, J. R. Torregrosa (1991)

Collectanea Mathematica

In this paper we prove that the geometrical notions of Rotundity and Uniform Rotundity of the norm in a Banach space are stable for the generalized Banach products.

Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces

Victor Klee, Libor Veselý, Clemente Zanco (1996)

Studia Mathematica

For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class...

Roughness of two norms on Musielak-Orlicz function spaces

Jimin Zheng, Lihuan Sun, Yun'an Cui (2008)

Banach Center Publications

In this paper, the criteria of strong roughness, roughness and pointwise roughness of Orlicz norm and Luxemburg norm on Musielak-Orlicz function spaces are obtained.

RUC systems in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, F. A. Sukochev (2002)

Studia Mathematica

We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.

Schauder bases and the bounded approximation property in separable Banach spaces

Jorge Mujica, Daniela M. Vieira (2010)

Studia Mathematica

Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties s u p n ∈ ℕ | | T ₙ | | ≤ λ + ϵ and l i m s u p n → ∞ | | T ₙ | | ≤ λ . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.

Schauder decompositions and multiplier theorems

P. Clément, B. de Pagter, F. Sukochev, H. Witvliet (2000)

Studia Mathematica

We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for L p -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.

Schroeder-Bernstein Quintuples for Banach Spaces

Elói Medina Galego (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Let X and Y be two Banach spaces, each isomorphic to a complemented subspace of the other. In 1996, W. T. Gowers solved the Schroeder-Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain necessary and sufficient conditions on the quintuples (p,q,r,s,t) in ℕ for X to be isomorphic to Y whenever ⎧ X X p ⊕ Y q , ⎨ ⎩ Y t X r ⊕ Y s . Such quintuples are called Schroeder-Bernstein quintuples for Banach spaces and they yield a unification of the known decomposition...

Second derivatives of norms and contractive complementation in vector-valued spaces

Bas Lemmens, Beata Randrianantoanina, Onno van Gaans (2007)

Studia Mathematica

We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces ℓ p ( X ) , where X is a Banach space with a 1-unconditional basis and p ∈ (1,2) ∪ (2,∞). If the norm of X is twice continuously differentiable and satisfies certain conditions connecting the norm and the notion of disjointness with respect to the basis, then we prove that every 1-complemented subspace of ℓ p ( X ) admits a basis of mutually disjoint elements. Moreover, we show that every contractive projection is then...

Currently displaying 2261 – 2280 of 3166