LEADER 04015nam 2200673Ia 450 001 9910964777403321 005 20251116203754.0 010 $a9786611919511 010 $a9781281919519 010 $a1281919519 010 $a9789812774484 010 $a9812774483 035 $a(CKB)1000000000413287 035 $a(DLC)2006283691 035 $a(StDuBDS)AH24684523 035 $a(SSID)ssj0000252681 035 $a(PQKBManifestationID)11220684 035 $a(PQKBTitleCode)TC0000252681 035 $a(PQKBWorkID)10185344 035 $a(PQKB)10390438 035 $a(MiAaPQ)EBC1681732 035 $a(WSP)00005993 035 $a(Au-PeEL)EBL1681732 035 $a(CaPaEBR)ebr10201377 035 $a(CaONFJC)MIL191951 035 $a(OCoLC)879025635 035 $a(Perlego)849224 035 $a(BIP)13341420 035 $a(EXLCZ)991000000000413287 100 $a20060927d2006 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStructure of Hilbert space operators /$fChunlan Jiang, Zongyao Wang 205 $a1st ed. 210 $aHackensack, NJ $cWorld Scientific$d2006 215 $a1 online resource (x, 248 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9789812566164 311 08$a9812566163 320 $aIncludes bibliographical references (p. 241-246) and index. 327 $aPreface -- 1. Background. 1.1. Banach algebra. 1.2. K-theory of Banach algebra. 1.3. The basic of complex geometry. 1.4. Some results on Cowen-Douglas operators. 1.5. Strongly irreducible operators. 1.6. Compact perturbation of operators. 1.7. Similarity orbit theorem. 1.8. Toeplitz operator and Sobolev space -- 2. Jordan standard theorem and K[symbol]-group. 2.1. Generalized Eigenspace and minimal idempotents. 2.2. Similarity invariant of matrix. 2.3. Remark -- 3. Approximate Jordan theorem of operators. 3.1. Sum of strongly irreducible operators. 3.2. Approximate Jordan decomposition theorem. 3.3. Open problems. 3.4. Remark -- 4. Unitary invariant and similarity invariant of operators. 4.1. Unitary invariants of operators. 4.2. Strongly irreducible decomposition of operators and similarity invariant: K[symbol]-group. 4.3. (SI) decompositions of some classes of operators. 4.4. The commutant of Cowen-Douglas operators. 4.5. The Sobolev disk algebra. 4.6. The operator weighted shift. 4.7. Open problem. 4.8. Remark -- 5. The similarity invariant of Cowen-Douglas operators. 5.1. The Cowen-Douglas operators with index 1. 5.2. Cowen-Douglas operators with index n. 5.3. The commutant of Cowen-Douglas operators. 5.4. The commutant of a classes of operators. 5.5. The (5I) representation theorem of Cowen-Douglas operators. 5.6. Maximal ideals of the commutant of Cowen-Douglas operators. 5.7. Some approximation theorem. 5.8. Remark. 5.9. Open problem -- 6. Some other results about operator structure. 6.1. K[symbol]-group of some Banach algebra. 6.2. Similarity and quasisimilarity. 6.3. Application of operator structure theorem. 6.4. Remark. 6.5. Open problems. 330 $aThis book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen?Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen?Douglas operators by using K-theory, complex geometry and operator algebra tools. 606 $aHilbert space 606 $aLinear operators 615 0$aHilbert space. 615 0$aLinear operators. 676 $a515.733 700 $aJiang$b Chunlan$0549460 701 $aWang$b Zongyao$0549461 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910964777403321 996 $aStructure of Hilbert space operators$94476635 997 $aUNINA