Real Analytic Curves in Fréchet Spaces and Their Duals.
Real closed rings, I. Residue rings of rings of continuous functions
Real interpolation for families of Banach spaces
We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for spaces and the recent method of Cobos-Peetre.
Real interpolation for families of Banach spaces (II).
Real interpolation for non-distant Marcinkiewicz spaces.
We describe the real interpolation spaces between given Marcinkiewicz spaces that have fundamental functions of the form t1/q (ln (e/t)a with the same exponent q. The spaces thus obtained are used for the proof of optimal interpolation theorem from [7], concerning spaces L∞,a,E.
Real method of interpolation on subcouples of codimension one
We find necessary and sufficient conditions under which the norms of the interpolation spaces and are equivalent on N, where N is the kernel of a nonzero functional ψ ∈ (X₀ ∩ X₁)* and is the normed space N with the norm inherited from (i = 0,1). Our proof is based on reducing the problem to its partial case studied by Ivanov and Kalton, where ψ is bounded on one of the endpoint spaces. As an application we completely resolve the problem of when the range of the operator (S denotes the...
Realcompactness and spaces of vector-valued functions
It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating...
Rearrangement and continuity properties of functions on spaces of homogeneous type
Rearrangement and convergence in spaces of measurable functions.
Recent developments in the theory of function spaces
Recent developments in the theory of function spaces with dominating mixed smoothness
The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...
Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if...
Reflected double layer potentials and Cauchy's operators
Necessary and sufficient conditions are given for the reflected Cauchy's operator (the reflected double layer potential operator) to be continuous as an operator from the space of all continuous functions on the boundary of the investigated domain to the space of all holomorphic functions on this domain (to the space of all harmonic functions on this domain) equipped with the topology of locally uniform convergence.
Reflexive Orlicz spaces have uniformly normal structure
We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.
Reflexive subspaces of some Orlicz spaces
We show that when the conjugate of an Orlicz function ϕ satisfies the growth condition Δ⁰, then the reflexive subspaces of are closed in the L¹-norm. For that purpose, we use (and give a new proof of) a result of J. Alexopoulos saying that weakly compact subsets of such have equi-absolutely continuous norm.
Reflexivität von Räumen stetiger affiner Funktionen.
Reflexivity and kernels in infinite dimensional holomorphy
Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces
2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.For weakly compact subsets of Hilbert spaces K, we study the existence of totally disconnected spaces L, such that C(K) is isomorphic to C(L). We prove that the space C(BH ) admits a Pełczyński decomposition and we provide a starshaped weakly compact K, subset of BH with non-empty interior in the norm topology, and such that C(K) ~= C(L) with L totally disconnected.Research partially supported by EPEAEK program “Pythagoras”....
Regular vector lattices of continuous functions and Korovkin-type theorems-Part II
By applying the results of the first part of the paper, we establish some Korovkin-type theorems for continuous positive linear operators in the setting of regular vector lattices of continuous functions. Moreover, we present simple methods to construct Korovkin subspaces for finitely defined operators and for the identity operator and we determine those classes of operators which admit finite-dimensional Korovkin subspaces. Finally, we give a Korovkin-type theorem for continuous positive projections....
Regular vector lattices of continuous functions and Korovkin-type theorems-Part I
We introduce and study a new class of locally convex vector lattices of continuous functions on a locally compact Hausdorff space, which we call regular vector lattices. We investigate some general properties of these spaces and of the subspaces of so-called generalized affine functions. Moreover, we present some Korovkin-type theorems for continuous positive linear operators; in particular, we study Korovkin subspaces for finitely defined operators, for the identity operator and for positive...