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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0281045-8
PII: S 0002-9947(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