LEADER 04139nam 2200637Ia 450 001 9910453455903321 005 20200520144314.0 010 $a3-7643-8726-2 024 7 $a10.1007/978-3-7643-8726-6 035 $a(CKB)1000000000546236 035 $a(EBL)417023 035 $a(OCoLC)304518938 035 $a(SSID)ssj0000125984 035 $a(PQKBManifestationID)11134069 035 $a(PQKBTitleCode)TC0000125984 035 $a(PQKBWorkID)10030082 035 $a(PQKB)10400557 035 $a(DE-He213)978-3-7643-8726-6 035 $a(MiAaPQ)EBC417023 035 $a(PPN)130186341 035 $a(Au-PeEL)EBL417023 035 $a(CaPaEBR)ebr10267043 035 $a(EXLCZ)991000000000546236 100 $a20080310d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCommutative algebras of Toeplitz operators on the Bergman space$b[electronic resource] /$fNikolai L. Vasilevski 205 $a1st ed. 2008. 210 $aBasel $cBirkha?user ;$a[London $cSpringer, distributor]$d2008 215 $a1 online resource (443 p.) 225 1 $aOperator theory, advances and applications ;$vv. 185 300 $aDescription based upon print version of record. 311 $a3-7643-8725-4 320 $aIncludes bibliographical references and index. 327 $aPreliminaries -- Prologue -- Bergman and Poly-Bergman Spaces -- Bergman Type Spaces on the Unit Disk -- Toeplitz Operators with Commutative Symbol Algebras -- Toeplitz Operators on the Unit Disk with Radial Symbols -- Toeplitz Operators on the Upper Half-Plane with Homogeneous Symbols -- Anatomy of the Algebra Generated by Toeplitz Operators with Piece-wise continuous Symbols -- Commuting Toeplitz Operators and Hyperbolic Geometry -- Weighted Bergman Spaces -- Commutative Algebras of Toeplitz Operators -- Dynamics of Properties of Toeplitz Operators with Radial Symbols -- Dynamics of Properties of Toeplitz Operators on the Upper Half-Plane: Parabolic Case -- Dynamics of Properties of Toeplitz Operators on the Upper Half-Plane: Hyperbolic Case. 330 $aThis book is devoted to the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitz operators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields a powerful research tool giving direct access to the majority of the important properties of the Toeplitz operators studied herein, such as boundedness, compactness, spectral properties, invariant subspaces. The presence and exploitation of these spectral type representations forms the core for many results presented in the book. Among other results it contains a criterion of when the algebras are commutative on each commonly considered weighted Bergman space together with their explicit descriptions; a systematic study of Toeplitz operators with unbounded symbols; a clarification of the difference between compactness of commutators and semi-commutators of Toeplitz operators; the theory of Toeplitz and related operators with symbols having more than two limit values at boundary points; and a kind of semi-classical analysis of spectral properties of Toeplitz operators. The book is addressed to a wide audience of mathematicians, from graduate students to researchers, whose primary interests lie in complex analysis and operator theory. . 410 0$aOperator theory, advances and applications ;$vv. 185. 606 $aBergman spaces 606 $aCommutative algebra 606 $aToeplitz operators 608 $aElectronic books. 615 0$aBergman spaces. 615 0$aCommutative algebra. 615 0$aToeplitz operators. 676 $a515.7246 700 $aVasilevski$b Nikolai$0504977 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453455903321 996 $aCommutative algebras of Toeplitz operators on the Bergman space$9807201 997 $aUNINA