By Kehe Zhu
ISBN-10: 0821839659
ISBN-13: 9780821839652
This e-book covers Toeplitz operators, Hankel operators, and composition operators on either the Bergman area and the Hardy area. The surroundings is the unit disk and the most emphasis is on dimension estimates of those operators: boundedness, compactness, and club within the Schatten periods. such a lot effects predicament the connection among operator-theoretic homes of those operators and function-theoretic houses of the inducing symbols. therefore a significant portion of the ebook is dedicated to the learn of analytic functionality areas similar to the Bloch house, Besov areas, and BMOA, whose parts are for use as symbols to urge the operators we learn. The e-book is meant for either examine mathematicians and graduate scholars in complicated research and operator thought. the necessities are minimum; a graduate path in every one of actual research, complicated research, and practical research should still sufficiently organize the reader for the booklet. routines and bibliographical notes are supplied on the finish of every bankruptcy. those notes will element the reader to extra effects and difficulties. Kehe Zhu is a professor of arithmetic on the nation college of latest York at Albany. His past books comprise concept of Bergman areas (Springer, 2000, with H. Hedenmalm and B. Korenblum) and areas of Holomorphic services within the Unit Ball (Springer, 2005). His present study pursuits are holomorphic functionality areas and operators performing on them.
Read or Download Operator theory in function spaces PDF
Similar functional analysis books
This graduate-level textual content bargains a survey of the most rules, techniques, and strategies that represent nonlinear practical research. It positive factors wide observation, many examples, and engaging, demanding workouts. subject matters comprise measure mappings for countless dimensional areas, the inverse functionality idea, the implicit functionality concept, Newton's tools, and lots of different topics.
A Basis Theory Primer: Expanded Edition
The classical topic of bases in Banach areas has taken on a brand new existence within the glossy improvement of utilized harmonic research. This textbook is a self-contained creation to the summary concept of bases and redundant body expansions and its use in either utilized and classical harmonic research. The 4 components of the textual content take the reader from classical sensible research and foundation thought to fashionable time-frequency and wavelet idea.
INVERSE STURM-LIOUVILLE PROBLEMS AND THEIR APPLICATIONS
This publication offers the most effects and strategies on inverse spectral difficulties for Sturm-Liouville differential operators and their purposes. Inverse difficulties of spectral research consist in recuperating operators from their spectral features. Such difficulties frequently look in arithmetic, mechanics, physics, electronics, geophysics, meteorology and different branches of average sciences.
- Advanced Real Analysis
- Singular Integrals and Differentiability Properties of Functions
- Dimensions of Spaces of Siegel Cusp Forms of Degree Two and Three
- Complex Function Theory
Extra info for Operator theory in function spaces
Sample text
Also its linear span is dense in H, since the linear span coincides with that of {Wj:j2: 1}. We claim that, for each that f E H, Pkf -t f as k ~ 00. 38) IIfl12 = IJPkfl1 2+ Ilf - Pkfl1 2 2: IJPkfl12 = ~ I(J, uj)12. j=l W, We also see that, if n 2: k, then IJPnf - Pk f 112 = I:k 25) d(x, K) = inf {llx - yll : y E K}. 4. 7. If K cHis a nonempty, closed. convex set in a Hilbert space H and if x E H, then there ~s a unique z E K such that d(x, K) = Ilx - zll· Proof. We can pick Yn E K such that Ilx - Y'lii ---+ d = d(x, K). 24) with u = Ym - x, 'U = X - Yn, to get Since K b convex, (Yn + Ym)/2 lim sup llYn E K, so ilx - (Yn - Ymll'2 :s 2d'2 + 2d'2 - + Ym)/211 2': d. 4d'2 Therefore :s 0, mn-oo which implies convergence. In particular, this result applies when K i& a closed linear subspace of H. 30) becomes (K ~ ) ~ = K. Using the orthogonal projection discussed above, we can establish the following result. 8. If H is a Hilbert space and