70 research outputs found
Applications of Hilbert Module Approach to Multivariable Operator Theory
A commuting -tuple of bounded linear operators on a
Hilbert space \clh associate a Hilbert module over
in the following sense: where and
. A companion survey provides an introduction to the theory
of Hilbert modules and some (Hilbert) module point of view to multivariable
operator theory. The purpose of this survey is to emphasize algebraic and
geometric aspects of Hilbert module approach to operator theory and to survey
several applications of the theory of Hilbert modules in multivariable operator
theory. The topics which are studied include: generalized canonical models and
Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert
spaces, a class of simple submodules and quotient modules of the Hardy modules
over polydisc, commutant lifting theorem, similarity and free Hilbert modules,
left invertible multipliers, inner resolutions, essentially normal Hilbert
modules, localizations of free resolutions and rigidity phenomenon.
This article is a companion paper to "An Introduction to Hilbert Module
Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in
Handbook of Operator Theory, Springe
Geometric maximal operators and BMO on product bases
We consider the problem of the boundedness of maximal operators on BMO on
shapes in . We prove that for bases of shapes with an engulfing
property, the corresponding maximal function is bounded from BMO to BLO,
generalising a known result of Bennett for the basis of cubes. When the basis
of shapes does not possess an engulfing property but exhibits a product
structure with respect to lower-dimensional shapes coming from bases that do
possess an engulfing property, we show that the corresponding maximal function
is bounded from BMO to a space we define and call rectangular BLO
Changes in mastectomy rates at a Brazilian public hospital over 20 years (1989 to 2008)
Abstract, weighted, and multidimensional Adamjan-Arov-Krein theorems, and the singular numbers of Sarason commutants
Nehari and Nevanlinna-Pick Problems and Holomorphic Extensions in the Polydisk in Terms of Restricted BMO
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