-bounded semigroups and implicit evolution equations.
-spaces and applications to extrapolation theory
We investigate a scale of -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with --estimates, and arrives at --estimates, or more generally, at estimates between K-functionals from interpolation theory.
is generated in strong operator topology by two of its elements
Back to RS-SR spectral theory
Let X, Y be Banach spaces, S: X → Y and R: Y → X be bounded operators. We investigate common spectral properties of RS and SR. We then apply the result obtained to extensions, Aluthge transforms and upper triangular operator matrices.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Backward Aluthge iterates of a hyponormal operator and scalar extensions
Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar.
Backward Euler type methods for parabolic integro-differential equations in Banach space
Backward extensions of hyperexpansive operators
The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.
Bad properties of the Bernstein numbers
We show that the classes associated with the Bernstein numbers bₙ fail to be operator ideals. Moreover, for 1/r = 1/p + 1/q.
Bade's theorem on the uniformly closed algebra generated by a Boolean algebra
Ball intersection model for Fejér zones of convex closed sets
Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.
Ball remotal subspaces of Banach spaces
We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X).
Banach Algebra of Bounded Complex-Valued Functionals
In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.
Banach ideals of p-compact operators.
Banach ideals on Hilbert spaces
Banach limits in vector lattices
Banach manifolds of algebraic elements in the algebra (H) of bounded linear operatorsof bounded linear operators
Given a complex Hilbert space H, we study the manifold of algebraic elements in . We represent as a disjoint union of closed connected subsets M of Z each of which is an orbit under the action of G, the group of all C*-algebra automorphisms of Z. Those orbits M consisting of hermitian algebraic elements with a fixed finite rank r, (0< r<∞) are real-analytic direct submanifolds of Z. Using the C*-algebra structure of Z, a Banach-manifold structure and a G-invariant torsionfree affine...
Banach principle in the space of τ-measurable operators
We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.
Banach spaces and operators which are nearly uniformly convex [Book]
Banach spaces in which all multilinear forms are weakly sequentially continuous
We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this gives an...