Bulletin of the American Mathematical Society

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MathSciNet review: 838794

Book Information

Author(s): Domingo Herrero
Title: Approximation of Hilbert space operators,
Additional book information: Pitman Publishing Inc., Boston, 1982, xiii + 255 pp., $23.95. ISBN 0-273-08579-4

Author(s): Constantin Apostol
Title: Volume II Approximation of Hilbert space operators,
Additional book information: Lawrence Fialkow, Domingo Herrero and Dan Voiculescu, Pitman Publishing Inc., Boston, 1984, x + 524 pp., $29.95. ISBN 0-273-08641-3

[A1] C. Apostol, On the norm-closure of nilpotents, Rev. Roumaine Math. Pures Appl. 19 (1974), 277-282. MR 361875

[A2] C. Apostol, On the norm-closure of nilpotents. III, Rev. Roumaine Math. Pures Appl. 21 (1976), 143-153. MR 417829

[A3] C. Apostol, Universal quasinilpotent operators, Rev. Roumaine Math. Pures Appl. 25 (1980), 135-138. MR 577021

[AF] C. Apostol and C. Foiaş, On the distance to bi-quasitriangular operators, Rev. Roumaine Math. Pure Appl. 20 (1975), 261-265. MR 370238

[AFP] C. Apostol, C. Foiaş and C. M. Pearcy, That quasinilpotent operators are norm-limits of nilpotent operators revisited, Proc. Amer, Math. Soc. 73 (1979), 61-64. MR 512059

[AFV1] C. Apostol, C. Foiaş and D. Voiculescu, Some results on quasitriangular operators. II-VI, Rev. Roumaine Math. Pures Appl. 18 (1973), 159-181, 309-324, 487-514. MR 333785

[AFV2] C. Apostol, C. Foiaş and D. Voiculescu, On the norm-closure of nilpotents. II, Rev. Roumaine Math. Pures Appl. 19 (1974), 549-577. MR 355657

[AHV] C. Apostol, D. A. Herrero and D. Voiculescu, The closure of the similarity orbit of a Hilbert space operator, (NS) Bull. Amer. Math. Soc. 6 (1982), 421-426. MR 648526

[AV] C. Apostol and D. Voiculescu, On a problem of Halmos, Rev. Roumaine Math. Pures Appl. 19 (1974), 283-284. MR 338810

[AS] N. Aronszajn and K. T. Smith, Invariant subspaces of completely continuous operators, Ann. of Math. (2) 60 (1954), 345-350. MR 65807

[BH1] J. Barria and D. A. Herrero, Closure of similarity orbits of Hilbert space operators. IV. Normal operators, J. London Math. Soc. (2) 17 (1978), 525-536. MR 512781

[BH2] J. Barria and D. A. Herrero, Closure of similarity orbits of nilpotent operators. I. Finite rank operators, J. Operator Theory 1 (1979), 177-185. MR 532873

[B1] I. D. Berg, An extension of the Weyl-von Neumann theorem to normal operators, Trans. Amer. Math. Soc. 160 (1971), 365-371. MR 283610

[B2] I. D. Berg, On approximation of normal operators by weighted shifts, Michigan Math. J. 21 (1974), 377-383. MR 370235

[BDF1] L. G. Brown, R. G. Douglas and P. A. Fillmore, Extensions of C, Bull. Amer. Math. Soc. 79 (1973), 973-978. MR 346540

[BDF2] L. G. Brown, R. G. Douglas and P. A. Fillmore, Extensions of C, Ann. of Math. (2) 105 (1977), 265-324. MR 458196

[DS] N. Dunford and J. T. Schwartz, Linear operators, Part II: Spectral theory. Self-adjoint operators in Hilbert space, Interscience, New York and London, 1963. MR 188745

[FPV] C. Foiaş, C. M. Pearcy and D. Voiculescu, The staircase representation of a biquasitriangular operator, Michigan Math. J. 22 (1975), 343-352. MR 405146

[Ha1] P. R. Halmos, Quasitriangular operators, Acta. Sci. Math. (Szeged) 29 (1968), 283-393. MR 234310

[Ha2] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 270173

[Ha3] P. R. Halmos, Ten years in Hilbert space, Integral Equations Operators Theory 2 (1979), 529-564. MR 555777

[H1] D. A. Herrero, Normal limits of nilpotent operators, Indiana Univ. Math. J. 23 (1974), 1097-1108. MR 350476

[H2] D. A. Herrero, Universal quasinilpotent operators, Acta Sci. Math. (Szeged) 38 (1976), 291-300. MR 442728

[R] G.-C. Rota, On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469-472. MR 112040

[S] W. Sikonia, The von Neumann converse of Weyl's theorem, Indiana Univ. Math. J. 21 (1971), 121-123. MR 285928

[V1] D. Voiculescu, A non-commutative Weyl-von Neumann theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), 97-113. MR 415338

[V2] D. Voiculescu, Norm-limits of algebraic operators, Rev. Roumaine Math. Pures Appl. 19 (1974), 371-378. MR 343082

[W] H. Weyl, Über beschrankte quadratische Formen deren Differenzvollstetig ist, Rend. Circ. Mat. Palermo 27 (1909), 373-392.

Review Information:
Journal: Bull. Amer. Math. Soc. 15 (1986), 91-98.
DOI: 10.1090/S0273-0979-1986-15447-9
PII: S 0273-0979(1986)15447-9

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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