## Analysis of Toeplitz OperatorsSince the late 1980s, Toeplitz operators and matrices have remained a ?eld of extensive research and the development during the last nearly twenty years is impressive. One encounters Toeplitz matrices in plenty of applications on the one hand, and Toeplitz operators con?rmed their role as the basic elementary building blocks of more complicated operators on the other. Several monographs on Toeplitz and Hankel operators were written d- ing the last decade. These include Peller’s grandiose book on Hankel ope- tors and their applications and Nikolski’s beautiful easy reading on operators, functions, and systems, with emphasis on topics connected with the names of Hardy, Hankel, and Toeplitz. They also include books by the authors together withHagen,Roch,Yu.Karlovich,Spitkovsky,Grudsky,andRabinovich.Thus, results, techniques, and developments in the ?eld of Toeplitz operators are now well presented in the monographic literature. Despite these competitive works, we felt that large parts of the ?rst edition of the present monograp- whichismeanwhileoutofstock-havenotlosttheirfascinationandrelevance. Moreover, the ?rst edition has received a warm reception by many colleagues and became a standard reference. This encouraged us to venture on thinking about a second edition, and we are grateful to the Springer Publishing House for showing an interest in this. |

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### Contents

IX | 36 |

X | 38 |

XI | 41 |

XII | 45 |

XIII | 49 |

XIV | 52 |

XV | 57 |

XVI | 64 |

XVII | 71 |

XVIII | 77 |

XIX | 85 |

XX | 99 |

XXI | 103 |

XXII | 110 |

XXIII | 119 |

XXIV | 128 |

XXV | 140 |

XXVI | 149 |

XXVII | 152 |

XXVIII | 157 |

XXIX | 166 |

XXX | 169 |

XXXI | 171 |

XXXII | 178 |

XXXIII | 187 |

XXXIV | 191 |

XXXV | 211 |

XXXVI | 217 |

XXXVII | 226 |

XXXVIII | 240 |

XXXIX | 244 |

XL | 249 |

XLI | 253 |

XLII | 254 |

XLIII | 264 |

XLIV | 267 |

XLV | 277 |

XLVI | 281 |

XLVII | 283 |

XLVIII | 287 |

XLIX | 293 |

L | 297 |

LI | 308 |

LX | 378 |

LXI | 389 |

LXII | 394 |

LXIII | 400 |

LXIV | 408 |

LXV | 417 |

LXVI | 421 |

LXVII | 428 |

LXVIII | 438 |

LXIX | 448 |

LXX | 454 |

LXXI | 461 |

LXXII | 470 |

LXXIII | 475 |

LXXIV | 481 |

LXXV | 486 |

LXXVI | 488 |

LXXVII | 492 |

LXXVIII | 497 |

LXXIX | 501 |

LXXX | 504 |

LXXXI | 513 |

LXXXII | 520 |

LXXXIII | 525 |

LXXXIV | 529 |

LXXXV | 533 |

LXXXVI | 537 |

LXXXVII | 543 |

LXXXVIII | 554 |

LXXXIX | 558 |

XC | 566 |

XCI | 570 |

XCII | 572 |

XCIII | 582 |

XCIV | 592 |

XCV | 595 |

XCVI | 605 |

XCVII | 611 |

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### Common terms and phrases

analogously analytic Anxn approximate identity argument B¨ottcher Banach algebra Banach space belongs Blaschke product bounded C*-algebra C*-subalgebra Cl Remark closed subalgebra closed two-sided ideal compact operator complex numbers constant containing continuous converges Corollary deduce define denote Dn(a equals exists finite ﬁrst formula Fourier coefficient Fredholm G L^xN G M(B G Mp G PC G QC Gelfand Gelfand transform given Gohberg Hankel operators Hence Hilbert space homeomorphic implies index zero invertible isometric isomorphism kernel Khvedelidze weight Krupnik left-invertible Lemma Let a G limsup linear locally sectorial mapping matrix function maximal antisymmetric set maximal ideal maximal ideal space norm Note Poisson kernel proof of Proposition proof of Theorem Proof.(a proved real-valued recall resp satisfying sequence Silbermann Spitkovsky suppose symbols Tn(a Toeplitz operators trace class Widom Wiener-Hopf