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Reine Angew. MR 28 ; errata MR 30, MR 7. Brown, P. Halmos, and A. Szeged 26 , MR 32 MR 8. Math Mech. MR 33 MR 9. MR Deckard, R. Douglas, and C.


Pearcy, On invariant subspaces of quasitriangular operators , Amer. Douglas and C. Pearcy, A characterization of thin operators , Acta Sci. Szeged 29 , MR 38 Pearcy, A note on quasitriangular operators , Duke Math. Dunford, A survey of the theory of spectral operators , Bull. MR 21 Fillmore and D. Topping, Sums of irreducible operators , Proc. Foguel, A counterexample to a problem of Sz.

MR 29 Gellar, Cyclic vectors and parts of the spectrum of a weighted shift , Trans. MR 11, Halmos, Normal dilations and extensions of operators , Summa Brasil. MR 13, Halmos, On Foguel's answer to Nagy's question , Proc.

A Hilbert Space Problem Book

MR 34 Halmos, Irreducible operators , Michigan Math. Continuity of norm Semicontinuity of operator norm Continuity of adjoint Continuity of multiplication. Separate continuity of multiplication Sequential continuity of multiplication Weak sequential continuity of squaring Weak convergence Spectrum of a diagonal operator. Increasing sequences of Hermitian operators Square roots Infimum of two projections.

A Hilbert Space Problem Book (2nd ed.)

Decreasing squares Polynomially diagonal operators Continuity of the functional calculus. Partial isometries. Reducing subspaces of normal operators Products of symmetries Unilateral shift versus normal operators. Square root of shift Commutant of the bilateral shift i47 Commutant of the unilateral shift.

Commutant of the unilateral shift as limit Characterization of isometries. Distance from shift to unitary operators Square roots of shifts. Shifts as universal operators Similarity to parts of shifts.

4 3 Hilbert spaces

Unilateral shift. Structure of the set of eigenvectors. Spectrum of a functional multiplication.

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Nonemptiness of spectra. Spectral radius. Weighted shifts. Similarity of weighted shifts.

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Norm and spectral radius of a weighted shift. Normal compact operators HilbertSchmidt operators. Compact versus HilbertSchmidt. Unbounded Voltcrra kernels Volterra integration operator. Skewsymmetric Volterra operator Norm 1 spectrum.

A Hilbert Space Problem Book - P.R. Halmos - Google книги

Algebras of normal operators Spectral measure of the unit disc. Ergodic theorem. Toeplitz products Compact Toeplitz products Spectral inclusion theorem for Toeplitz operators. Limits of operators of finite rank. Ideals of operators. Compactness on bases. Square root of a compact operator. Fredholm alternative. Range of a compact operator.

Atkinsons theorem. Perturbed spectrum. Shift modulo compact operators. Distance from shift to compact operators. Subnormal operators. Quasinormal invariants. Minimal normal extensions. Polynomials in the shift. Connectedness of invertible operators 70 Wandering subspaces. Bounded Volterra kernels 93 The Volterra integration. Numerical radius Continuity of numerical range Metric space of operators 52 Continuity of spectrum 53 Semicontinuity of spectrum 53 Continuity of spectral radius 54 Continuity of adjoint 56 Continuity of multiplication 56 Separate continuity of multiplication 57 Sequential continuity of multiplication 57 Square roots 58 Infimum of two projections 58