Woo Young Lee Lecture Notes on Operator Theory

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BIBLIOGRAPHY [Ist] [IW] [KL] [JeL] [La] [Le1] [Le2] V.I. Istratescu, On Weyl’s spectrum of an operator. I Rev. Roum. Math. Pures Appl. 17(1972), 1049–1059 T. Ito and T.K. Wong, Subnormality and quasinormality of Toeplitz operators, Proc. Amer. Math. Soc. 34(1972), 157–164 I.H. Kim and W.Y. <strong>Lee</strong>, On hyponormal Toeplitz operators with polynomial and symmetric-type symbols, Integral Equations Operator Theory, 32(1998), 216–233. I.H. Jeon and W.Y. <strong>Lee</strong>, On the Taylor-Browder spectrum, Commun. Korean Math. Soc. 11(1996), 997-1002 K.B. Laursen, Essential spectra through local spectral theory, Proc. Amer. math. Soc. 125(1997), 1425–1434 W.Y. <strong>Lee</strong>, Weyl’s theorem for operator matrices, Integral Equations Operator Theory, 32(1998), 319–331 W.Y. <strong>Lee</strong>, Weyl spectra of operator matrices, Proc. Amer. Math. Soc. 129(1)(2001), 131–138 [LL] W.Y. <strong>Lee</strong> and H.Y. <strong>Lee</strong>, On Weyl’s theorem, Math. Japon. 39 (1994), 545- 548 [LeL1] S.H. <strong>Lee</strong> and W.Y. <strong>Lee</strong>, On Weyl’s theorem (II), Math. Japon. 43(1996), 549–553 [LeL2] S.H. <strong>Lee</strong> and W.Y. <strong>Lee</strong>, A spectral mapping theorem for the Weyl spectrum, Glasgow Math. J. 38(1996), 61–64 [LeL3] S.H. <strong>Lee</strong> and W.Y. <strong>Lee</strong>, Hyponormal operators with rank-two selfcommutators (preprint) [McCYa] J.E. McCarthy and L. Yang, Subnormal operators and quadrature domains, Adv. Math. 127(1997), 52–72. [McCP] [Mor] [Mur] [NaT] S. McCullough and V. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107(1989), 187–195. B.B. Morrel, A decomposition for some operators, Indiana Univ. Math. J., 23(1973), 497-511. G. Murphy, C ∗ -algebras and operator theory, Academic press, New York, 1990. T. Nakazi and K. Takahashi, Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Trans. Amer. Math. Soc. 338(1993), 753–769 [Ne] J.D. Newburgh, The variation of spectra, Duke Math. J. 18(1951), 165–176 [Ni] N.K. Nikolskii, Treatise on the Shift Operators, Springer, New York, 1986 220
BIBLIOGRAPHY [Ob1] K.K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212 [Ob2] K.K. Oberai, On the Weyl spectrum II, Illinois J. Math. 21 (1977), 84-90 [Ol] [OTT] [Pe] [Pr] [Pru] R.F. Olin, Functional relationships between a subnormal operator and its minimal normal extension, Pacific. J. Math. 63(1976), 221-229. R.F. Olin, J.E. Thomson and T.T. Trent, Subnormal operators with finite rank self-commutator, (preprint 1990) C. Pearcy, Some recent developments in operator theory, C.B.M.S. Regional Conference Series in Mathematics, No. 36, Amer. Math. Soc., Providence, 1978 S. Prasanna, Weyl’s theorem and thin spectra, Proc. Indian Acad. Sci. 91(1982), 59–63 B. Prunaru, Invariant subspaces for polynomially hyponormal operators, Proc. Amer. Math. Soc. 125(1997), 1689–1691. [Pu1] M. Putinar, Linear analysis of quadrature domains, Ark. Mat., 33(1995), 357-376. [Pu2] [Pu3] [Pu4] [Put1] [Put2] [RR] [Sa] [Sch] [Shi] M. Putinar, Extremal solutions of the two-dimensional L-problem of moments, J. Funct. Anal., 136(1996), 331-364. M. Putinar, Extremal solutions of the two-dimensional L-problem of moments II, J. Approximation Theory, 92(1998), 32-58. M. Putinar, Linear analysis of quadrature domains III, J. Math. Anal. Appl., 239(1999), 101-117. C. Putnam, On the structure of semi-normal operators, Bull. Amer. Math. Soc., 69(1963), 818–819. C. Putnam, Commutation properties of Hilbert space operators and related topics, Springer, New York, 1967. H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, New York, 1973 D. Sarason, Generalized interpolation in H ∞ , Trans. Amer. Math. Soc. 127(1967), 179–203. I. Schur, Über Potenzreihen die im Innern des Einheitskreises beschränkt, J. Reine Angew. Math.147(1917), 205–232. A.L. Shields, Weighted shift operators and analytic function theory, Mathematical Surveys 13(1974), 49–128 (C. Pearcy, ed., Topics in Operator Theory, A.M.S. Providence, 1974) 221
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1 Graduate Texts ——————
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3 . Preface The present lectures ar
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CONTENTS 4.4 The Perturbations . .
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CHAPTER 1. FREDHOLM THEORY 1.2 Prel
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CHAPTER 1. FREDHOLM THEORY 1.3 Defi
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CHAPTER 1. FREDHOLM THEORY Corollar
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CHAPTER 1. FREDHOLM THEORY 1.5 The
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CHAPTER 1. FREDHOLM THEORY 1.6 Pert
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CHAPTER 1. FREDHOLM THEORY The Weyl
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CHAPTER 1. FREDHOLM THEORY Theorem
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CHAPTER 1. FREDHOLM THEORY Since T
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CHAPTER 1. FREDHOLM THEORY Proof. (
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CHAPTER 1. FREDHOLM THEORY The foll
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CHAPTER 1. FREDHOLM THEORY 1.10 Ess
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CHAPTER 1. FREDHOLM THEORY In fact,
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CHAPTER 1. FREDHOLM THEORY Since T
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CHAPTER 1. FREDHOLM THEORY 1.13 Com
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CHAPTER 2. WEYL THEORY finite dimen
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CHAPTER 2. WEYL THEORY We shall cal
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CHAPTER 2. WEYL THEORY If the condi
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CHAPTER 2. WEYL THEORY are called q
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CHAPTER 2. WEYL THEORY Proof. Let
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CHAPTER 2. WEYL THEORY which tends
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CHAPTER 2. WEYL THEORY We thus have
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CHAPTER 2. WEYL THEORY Proof. Newbu
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CHAPTER 2. WEYL THEORY Proof. By Le
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CHAPTER 2. WEYL THEORY Proof. If λ
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CHAPTER 2. WEYL THEORY Evidently K
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CHAPTER 2. WEYL THEORY Example 2.4.
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CHAPTER 2. WEYL THEORY (ii) σ(T )
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CHAPTER 2. WEYL THEORY 2.5 Weyl’s
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CHAPTER 2. WEYL THEORY A question a
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CHAPTER 2. WEYL THEORY (see [Ta2, T
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CHAPTER 2. WEYL THEORY Corollary 2.
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CHAPTER 2. WEYL THEORY Problem 2.4.
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CHAPTER 2. WEYL THEORY 76
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CHAPTER 3. HYPONORMAL AND SUBNORMAL
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CHAPTER 4. WEIGHTED SHIFTS Proof. T
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CHAPTER 4. WEIGHTED SHIFTS therefor
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CHAPTER 4. WEIGHTED SHIFTS Observe
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CHAPTER 4. WEIGHTED SHIFTS Since β
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CHAPTER 4. WEIGHTED SHIFTS then c(n
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where ⎧⎪⎨ ⎪ ⎩ q n = (α 2
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CHAPTER 4. WEIGHTED SHIFTS 4.4 The
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CHAPTER 4. WEIGHTED SHIFTS For exam
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CHAPTER 4. WEIGHTED SHIFTS One migh
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CHAPTER 4. WEIGHTED SHIFTS Theorem
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CHAPTER 4. WEIGHTED SHIFTS and c(n
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CHAPTER 4. WEIGHTED SHIFTS where by
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CHAPTER 4. WEIGHTED SHIFTS holds fo
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CHAPTER 4. WEIGHTED SHIFTS Theorem
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CHAPTER 4. WEIGHTED SHIFTS An immed
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CHAPTER 4. WEIGHTED SHIFTS 4.5 The
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CHAPTER 4. WEIGHTED SHIFTS In fact,
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CHAPTER 4. WEIGHTED SHIFTS H k+1 ,
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CHAPTER 4. WEIGHTED SHIFTS If h is
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CHAPTER 4. WEIGHTED SHIFTS are both
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CHAPTER 4. WEIGHTED SHIFTS Write f
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CHAPTER 4. WEIGHTED SHIFTS Proof. A
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CHAPTER 4. WEIGHTED SHIFTS We remem
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CHAPTER 4. WEIGHTED SHIFTS 156
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CHAPTER 5. TOEPLITZ THEORY Proof. (
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CHAPTER 5. TOEPLITZ THEORY 5.1.2 Ha
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CHAPTER 5. TOEPLITZ THEORY 5.1.3 To
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CHAPTER 5. TOEPLITZ THEORY satisfyi
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CHAPTER 5. TOEPLITZ THEORY Proof. I
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CHAPTER 5. TOEPLITZ THEORY Therefor
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Woo Young Lee Lecture Notes on Operator Theory

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