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Banach Embedding Properties of Non-Commutative LP-Spaces

Banach Embedding Properties of Non-Commutative LP-Spaces PDF Author: Uffe Haagerup
Publisher:
ISBN: 9781470403744
Category : Electronic books
Languages : en
Pages : 68

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Book Description
Introduction The modulus of uniform integrability and weak compactness in $L^1(\mathcal N)$ Improvements to the main theorem Complements on the Banach/operator space structure of $L^p(\mathcal N)$-spaces The Banach isomorphic classification of the spaces $L^p(\mathcal N)$ for $\mathcal N$ hyperfinite semi-finite $L^p(\mathcal N)$-isomorphism results for $\mathcal N$ a type III hyperfinite or a free group von Neumann algebra Bibliography

Banach Embedding Properties of Non-Commutative LP-Spaces

Banach Embedding Properties of Non-Commutative LP-Spaces PDF Author: Uffe Haagerup
Publisher:
ISBN: 9781470403744
Category : Electronic books
Languages : en
Pages : 68

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Book Description
Introduction The modulus of uniform integrability and weak compactness in $L^1(\mathcal N)$ Improvements to the main theorem Complements on the Banach/operator space structure of $L^p(\mathcal N)$-spaces The Banach isomorphic classification of the spaces $L^p(\mathcal N)$ for $\mathcal N$ hyperfinite semi-finite $L^p(\mathcal N)$-isomorphism results for $\mathcal N$ a type III hyperfinite or a free group von Neumann algebra Bibliography

Banach Embedding Properties of Non-Commutative $L^p$-Spaces

Banach Embedding Properties of Non-Commutative $L^p$-Spaces PDF Author: U. Haagerup
Publisher: American Mathematical Soc.
ISBN: 0821832719
Category : Mathematics
Languages : en
Pages : 82

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Book Description
Let $\mathcal N$ and $\mathcal M$ be von Neumann algebras. It is proved that $L DEGREESp(\mathcal N)$ does not linearly topologically embed in $L DEGREESp(\mathcal M)$ for $\mathcal N$ infinite, $\mathcal M$ finit

Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory

Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory PDF Author: Marius Junge
Publisher: American Mathematical Soc.
ISBN: 0821846558
Category : Mathematics
Languages : en
Pages : 168

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Book Description
Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.

Handbook of the Geometry of Banach Spaces

Handbook of the Geometry of Banach Spaces PDF Author:
Publisher: Elsevier
ISBN: 0080533507
Category : Mathematics
Languages : en
Pages : 873

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Book Description
Handbook of the Geometry of Banach Spaces

$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type

$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type PDF Author: Robert Denk
Publisher: American Mathematical Soc.
ISBN: 0821833782
Category : Mathematics
Languages : en
Pages : 130

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Book Description
The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.

Positive Definite Functions on Infinite-Dimensional Convex Cones

Positive Definite Functions on Infinite-Dimensional Convex Cones PDF Author: Helge Glöckner
Publisher: American Mathematical Soc.
ISBN: 0821832565
Category : Mathematics
Languages : en
Pages : 150

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Book Description
A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.

Yang-Mills Measure on Compact Surfaces

Yang-Mills Measure on Compact Surfaces PDF Author: Thierry Lévy
Publisher: American Mathematical Soc.
ISBN: 0821834290
Category : Mathematics
Languages : en
Pages : 144

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Book Description
In this memoir we present a new construction and new properties of the Yang-Mills measure in two dimensions. This measure was first introduced for the needs of quantum field theory and can be described informally as a probability measure on the space of connections modulo gauge transformations on a principal bundle. We consider the case of a bundle over a compact orientable surface. Our construction is based on the discrete Yang-Mills theory of which we give a full acount. We are able to take its continuum limit and to define a pathwise multiplicative process of random holonomy indexed by the class of piecewise embedded loops. We study in detail the links between this process and a white noise and prove a result of asymptotic independence in the case of a semi-simple structure group. We also investigate global Markovian properties of the measure related to the surgery of surfaces.

Shock-Wave Solutions of the Einstein Equations with Perfect Fluid Sources: Existence and Consistency by a Locally Inertial Glimm Scheme

Shock-Wave Solutions of the Einstein Equations with Perfect Fluid Sources: Existence and Consistency by a Locally Inertial Glimm Scheme PDF Author: Jeff Groah
Publisher: American Mathematical Soc.
ISBN: 082183553X
Category : Mathematics
Languages : en
Pages : 98

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Book Description
Demonstrates the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation.

The $RO(G)$-Graded Equivariant Ordinary Homology of $G$-Cell Complexes with Even-Dimensional Cells for $G=\mathbb {Z}/p$

The $RO(G)$-Graded Equivariant Ordinary Homology of $G$-Cell Complexes with Even-Dimensional Cells for $G=\mathbb {Z}/p$ PDF Author:
Publisher: American Mathematical Soc.
ISBN: 0821834614
Category :
Languages : en
Pages : 146

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Book Description

Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects

Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects PDF Author: Fabrizio Andreatta
Publisher: American Mathematical Soc.
ISBN: 0821836099
Category : Mathematics
Languages : en
Pages : 114

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Book Description
We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our methods are geometric - comparing holomorphic Hilbert modular forms with rational functions on a moduli scheme with level-$p$ structure, whose poles are supported on the non-ordinary locus.In the $p$-adic theory we study congruences between Hilbert modular forms. This applies to the study of congruences between special values of zeta functions of totally real fields. It also allows us to define $p$-adic Hilbert modular forms 'a la Serre' as $p$-adic uniform limit of classical modular forms, and compare them with $p$-adic modular forms 'a la Katz' that are regular functions on a certain formal moduli scheme. We show that the two notions agree for cusp forms and for a suitable class of weights containing all the classical ones. We extend the operators $V$ and $\Theta_\chi$ to the $p$-adic setting.