Annals of Functional Analysis最新文献

We obtain the boundedness for Hardy–Littlewood maximal operators on generalized Orlicz spaces in the abstract setting of measure spaces, which are equipped with a ball basis. Using this result, we establish an off-diagonal extrapolation and its applications, the boundedness for ({mathbb {B}})-valued linear bounded oscillation operators, on generalized Orlicz spaces.

The primary objective of this research is to use an extended Dobrushin ergodicity coefficient to explore residualities of the set of uniform P-ergodic Markov semigroups defined on abstract state spaces. Moreover, we investigate uniform mean ergodicities of Markov semigroups under the Doeblin’s Condition.

The purpose of this paper is to introduce (omega )-Chebyshev–Greedy and (omega )-partially greedy approximation classes and study their relation with (omega )-approximation spaces, where the latter are a generalization of the classical approximation spaces. The relation gives us sufficient conditions of when certain continuous embeddings imply different greedy-type properties. Along the way, we generalize a result by P. Wojtaszczyk as well as characterize semi-greedy Schauder bases in quasi-Banach spaces, generalizing a previous result by the first author.

Let A be a general expansive matrix. Let X be a ball quasi-Banach function space on (mathbb {R}^n), which supports both a Fefferman–Stein vector-valued maximal inequality and the boundedness of the powered Hardy–Littlewood maximal operator on its associate space. The authors first establish the boundedness of convolutional anisotropic Calderón–Zygmund operators on the Hardy space (H_X^A(mathbb {R}^n)). As an application, the authors also obtain the boundedness of Fourier multipliers satisfying anisotropic Mihlin conditions on (H_X^A(mathbb {R}^n)). All these results have a wide range of applications; in particular, when they are applied to Lebesgue spaces, all these results reduce back to the known best results and, even when they are applied to Lorentz spaces, variable Lebesgue spaces, Orlicz spaces, Orlicz-slice spaces, and local generalized Herz spaces, the obtained results are also new.

We prove that a closed convex subset of a Banach space is (super-)weakly compact if and only if it is (super)-ergodic. As a consequence, we deduce that super weakly compact sets are characterized by the fixed point property for continuous affine mappings. We also prove that the M-(fixed point property for affine isometries) implies the Banach-Saks property.

This paper studies matrices A in (M_n(mathbb C)) satisfying

where ({mathcal {B}}) is a C*-subalgebra of (M_n(mathbb C)) and (Vert cdot Vert ) denotes the operator norm. Such an A is called ({mathcal {B}})-minimal. The necessary and sufficient conditions for A to be ({mathcal {B}})-minimal are characterized, and a constructive method to obtain ({mathcal {B}})-minimal normal matrices is provided. Moreover, (bigoplus _{i=1}^k{mathcal {B}})-minimal normal matrices with anti-diagonal block form are studied.

In this paper, we pursue three aims. The first one is to apply Amitsur’s relations and radicals theory to the study of the lattices (hbox {Id}_{{A}}) of closed two-sided ideals of C*-algebras A. We show that many new and many well-known results about C*-algebras follow naturally from this approach. To use “relation-radical” approach, we consider various subclasses of the class ({mathfrak {A}}) of all C*-algebras, which we call C*-properties, as they often linked to some properties of C*-algebras. We consider C*-properties P consisting of CCR- and of GCR-algebras; of C*-algebras with continuous trace; of real rank zero, AF, nuclear C*-algebras, etc. Each P defines reflexive relations (ll _{{P}}) in all lattices (hbox {Id}_{A}.) Our second aim is to determine the hierarchy and interconnection between properties in ({mathfrak {A}}.) Our third aim is to study the link between the radicals of relations (ll _{{P}}) in the lattices (hbox {Id}_{{A}}) and the topological radicals on ({mathfrak {A}}.)

We introduce a notion of Morita equivalence for non-selfadjoint operator algebras equipped with a completely isometric involution (operator (*)-algebras). We then show that the unbounded Kasparov product by a Morita equivalence bimodule induces an isomorphism between equivalence classes of twisted spectral triples over Morita equivalent operator (*)-algebras. This leads to a tentative definition of unbounded bivariant K-theory and we prove that this bivariant theory is related to Kasparov’s bivariant K-theory via the Baaj-Julg bounded transform. Moreover, the unbounded Kasparov product provides a refinement of the usual interior Kasparov product. We illustrate our results by proving (C^1)-versions of well-known (C^*)-algebraic Morita equivalences in the context of hereditary subalgebras, conformal equivalences and crossed products by discrete groups.

We integrate in the framework of the semilocal trace formula two recent discoveries on the spectral realization of the zeros of the Riemann zeta function by introducing a semilocal analogue of the prolate wave operator. The latter plays a key role both in the spectral realization of the low lying zeros of zeta—using the positive part of its spectrum—and of their ultraviolet behavior—using the Sonin space which corresponds to the negative part of the spectrum. In the archimedean case the prolate operator is the sum of the square of the scaling operator with the grading of orthogonal polynomials, and we show that this formulation extends to the semilocal case. We prove the stability of the semilocal Sonin space under the increase of the finite set of places which govern the semilocal framework and describe their relation with Hilbert spaces of entire functions. Finally, we relate the prolate operator to the metaplectic representation of the double cover of ({text {SL}}(2,mathbb {R})) with the goal of obtaining (in a forthcoming paper) a second candidate for the semilocal prolate operator.