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Commutators, $ C\sp{k}$-classification, and similarity of operators


Author: Shmuel Kantorovitz
Journal: Trans. Amer. Math. Soc. 156 (1971), 193-218
MSC: Primary 47.40
DOI: https://doi.org/10.1090/S0002-9947-1971-0281045-8
MathSciNet review: 0281045
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Abstract: We generalize the results of our recent paper, The $ {C^k}$-classification of certain operators in $ {L_p}$. II, to the abstract setting of a pair of operators satisfying the commutation relation $ [M,N] = {N^2}$.


References [Enhancements On Off] (What's this?)

  • [1] N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354. MR 16, 142. MR 0063563 (16:142d)
  • [2] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] S. R. Foguel, The relations between a spectral operator and its scalar part, Pacific J. Math. 8 (1958), 51-65. MR 20 #3457. MR 0096976 (20:3457)
  • [4] E. Hille and R. S. Phillips, Functional analysis and semi-groups, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R. I., 1957. MR 19, 664. MR 0089373 (19:664d)
  • [5] G. K. Kalisch, On fractional integrals of pure imaginary order in $ {L_p}$, Proc. Amer. Math. Soc. 18 (1967), 136-139. MR 35 #7145. MR 0216310 (35:7145)
  • [6] -, Similarity invariants of certain operators in $ {L_p}$ (to appear).
  • [7] S. Kantorovitz, Operational calculus in Banach algebras for algebra-valued functions, Trans. Amer. Math. Soc. 110 (1964), 519-537. MR 28 #2457. MR 0159240 (28:2457)
  • [8] -, On the characterization of spectral operators, Trans. Amer. Math. Soc. 111 (1964), 152-181. MR 28 #3329. MR 0160115 (28:3329)
  • [9] -, Classification of operators by means of their operational calculus, Trans. Amer. Math. Soc. 115 (1965), 194-224. MR 33 #7855. MR 0199712 (33:7855)
  • [10] S. Kantorovitz, The $ {C^k}$-classification of certain operators in $ {L_p}$, Trans. Amer. Math. Soc. 132 (1968), 323-333. MR 37 #2033. MR 0226443 (37:2033)
  • [11] -, The $ {C^k}$-classification of certain operators in $ {L_p}$. II, Trans. Amer. Math. Soc. 146 (1969), 61-68.
  • [12] C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag, New York, 1967. MR 36 #707. MR 0217618 (36:707)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0281045-8
Keywords: $ {C^k}$-classification, similarity, commutation relation, holomorphic semigroup of operators, boundary group, Riemann-Liouville semigroup, Banach algebra, $ {C^k}$-operational calculus, spectrality, spectral operator, quasi-nilpotent
Article copyright: © Copyright 1971 American Mathematical Society

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