Operator Valued Hardy Spaces
Title | Operator Valued Hardy Spaces PDF eBook |
Author | Tao Mei |
Publisher | American Mathematical Soc. |
Total Pages | 78 |
Release | 2007 |
Genre | Mathematics |
ISBN | 0821839802 |
The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of noncommutative martingale inequalities. in this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it isproved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of theauthor's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1
Operator Valued Hardy Spaces and Related Subjects
Title | Operator Valued Hardy Spaces and Related Subjects PDF eBook |
Author | Tao Mei |
Publisher | |
Total Pages | |
Release | 2006 |
Genre | |
ISBN |
We give a systematic study of the Hardy spaces of functions with values in the non-commutative Lp-spaces associated with a semifinite von Neumann algebra M. This is motivated by matrix valued harmonic analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of non-commutative martingale inequalities. Our non-commutative Hardy spaces are defined by non-commutative Lusin integral functions. It is proved in this dissertation that they are equivalent to those defined by the non-commutative Littlewood-Paley G-functions. We also study the Lp boundedness of operator valued dyadic paraproducts and prove that their Lq boundedness implies their Lp boundedness for all 1
Hardy Classes and Operator Theory
Title | Hardy Classes and Operator Theory PDF eBook |
Author | Marvin Rosenblum |
Publisher | Courier Corporation |
Total Pages | 204 |
Release | 1997-01-01 |
Genre | Mathematics |
ISBN | 9780486695365 |
Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Topics include general theory of shift operators on a Hilbert space, use of lifting theorem to give a unified treatment of interpolation theorems of the Pick-Nevanlinna and Loewner types, more. Appendix. Bibliography. 1985 edition.
The Backward Shift on the Hardy Space
Title | The Backward Shift on the Hardy Space PDF eBook |
Author | Joseph A. Cima |
Publisher | American Mathematical Soc. |
Total Pages | 215 |
Release | 2000 |
Genre | Mathematics |
ISBN | 0821820834 |
Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, "parts" of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator. This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces H{p}. The characterization of the backward shift invariant subspaces of H{p} for 1
Operator Theory in Function Spaces
Title | Operator Theory in Function Spaces PDF eBook |
Author | Kehe Zhu |
Publisher | American Mathematical Soc. |
Total Pages | 368 |
Release | 2007 |
Genre | Mathematics |
ISBN | 0821839659 |
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori
Title | Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori PDF eBook |
Author | Xiao Xiong |
Publisher | American Mathematical Soc. |
Total Pages | 118 |
Release | 2018-03-19 |
Genre | |
ISBN | 1470428067 |
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative -torus (with a skew symmetric real -matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincaré type inequality for Sobolev spaces.
Shift Operators on the C[2]-valued Hardy Space
Title | Shift Operators on the C[2]-valued Hardy Space PDF eBook |
Author | |
Publisher | |
Total Pages | 16 |
Release | 2007 |
Genre | |
ISBN |