Basic Classes of Linear OperatorsThe present book is an expanded and enriched version ofthe textBasicOperator Theory, written by the first two authors more than twenty years ago. Since then the three ofus have used the basic operator theory text in various courses. This experience motivated us to update and improve the old text by including a wider variety ofbasic classes ofoperators and their applications. The present book has also been written in such a way that it can serve as an introduction to our previous booksClassesofLinearOperators, Volumes I and II. We view the three books as a unit. We gratefully acknowledge the support of the mathematical departments of Tel-Aviv University, the University of Maryland at College Park, and the Vrije Universiteit atAmsterdam. The generous support ofthe Silver Family Foundation is highly appreciated. Amsterdam, November 2002 The authors Introduction This elementary text is an introduction to functional analysis, with a strong emphasis on operator theory and its applications. It is designed for graduate and senior undergraduate students in mathematics, science, engineering, and other fields. |
Contents
III | xv |
IV | xvii |
V | 1 |
VI | 4 |
VII | 6 |
VIII | 9 |
IX | 11 |
X | 12 |
LXXXIV | 216 |
LXXXV | 221 |
LXXXVIII | 226 |
LXXXIX | 228 |
XC | 229 |
XCI | 230 |
XCII | 233 |
XCV | 234 |
XI | 14 |
XII | 15 |
XIII | 20 |
XIV | 22 |
XV | 25 |
XVI | 27 |
XVII | 28 |
XVIII | 30 |
XIX | 31 |
XX | 32 |
XXI | 34 |
XXIII | 47 |
XXV | 48 |
XXVI | 52 |
XXVII | 53 |
XXVIII | 56 |
XXIX | 59 |
XXX | 60 |
XXXI | 65 |
XXXII | 67 |
XXXIII | 69 |
XXXIV | 72 |
XXXV | 76 |
XXXVI | 77 |
XXXVII | 78 |
XXXVIII | 80 |
XXXIX | 87 |
XL | 92 |
XLI | 101 |
XLII | 104 |
XLIII | 105 |
XLIV | 114 |
XLV | 131 |
XLVIII | 137 |
XLIX | 139 |
L | 148 |
LI | 155 |
LII | 159 |
LIII | 162 |
LIV | 167 |
LVIII | 168 |
LIX | 170 |
LX | 171 |
LXI | 174 |
LXII | 176 |
LXIII | 178 |
LXIV | 179 |
LXV | 181 |
LXVI | 184 |
LXVII | 189 |
LXX | 193 |
LXXI | 196 |
LXXIII | 199 |
LXXV | 200 |
LXXVI | 202 |
LXXVII | 204 |
LXXVIII | 207 |
LXXIX | 210 |
LXXX | 211 |
LXXXI | 215 |
XCVI | 238 |
XCVII | 239 |
C | 240 |
CI | 242 |
CII | 244 |
CIII | 249 |
CIV | 250 |
CV | 255 |
CVII | 260 |
CVIII | 261 |
CIX | 263 |
CX | 268 |
CXI | 273 |
CXIII | 275 |
CXIV | 277 |
CXV | 279 |
CXVI | 282 |
CXVII | 284 |
CXVIII | 285 |
CXIX | 286 |
CXX | 289 |
CXXI | 291 |
CXXII | 292 |
CXXIII | 295 |
CXXV | 298 |
CXXVI | 299 |
CXXVII | 301 |
CXXVIII | 302 |
CXXIX | 306 |
CXXX | 309 |
CXXXI | 310 |
CXXXII | 313 |
CXXXV | 317 |
CXXXVI | 323 |
CXXXVII | 326 |
CXXXVIII | 332 |
CXXXIX | 336 |
CXL | 343 |
CXLIII | 348 |
CXLIV | 351 |
CXLV | 352 |
CXLVI | 355 |
CXLVII | 357 |
CL | 360 |
CLI | 368 |
CLII | 373 |
CLIII | 380 |
CLIV | 386 |
CLV | 391 |
CLVI | 397 |
CLIX | 398 |
CLX | 401 |
CLXI | 405 |
CLXIII | 407 |
CLXV | 411 |
CLXVI | 413 |
CLXVII | 415 |
417 | |
Other editions - View all
Basic Classes of Linear Operators Israel Gohberg,Seymour Goldberg,Marinus Kaashoek Limited preview - 2012 |
Basic Classes of Linear Operators Israel Gohberg,Seymour Goldberg,Marinus A Kaashoek No preview available - 2003 |
Basic Classes of Linear Operators Israel Gohberg,Seymour Goldberg,Marinus Kaashoek No preview available - 2003 |
Common terms and phrases
adjoint operator assume Banach space basic system bounded linear operator Chapter closed subspace codim compact operator compact self adjoint complex numbers complex valued function continuous Corollary corresponding Definition det(I dim Ker eigenvalues eigenvectors equal Example finite dimensional finite rank finite section method formula Fredholm operator given H₁ Hence Hilbert space implies inequality infinite inner product space integral operator invertible operator kernel function Laurent operator Lebesgue integrable left invertible left or right Lemma Ma,ß matrix operator on L2 operators of finite orthogonal projection orthonormal basis polynomial proof of Theorem Prove relative to zero right invertible sequence space H spectral theorem standard basis Suppose system of eigenvectors Theorem 4.1 theory Toeplitz operator unit circle vector space winding number y₁ απ