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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Commutators, $C^{k}$-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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Keywords: <IMG WIDTH="31" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" SRC="images/img8.gif" ALT="${C^k}$">-classification, similarity, commutation relation, holomorphic semigroup of operators, boundary group, Riemann-Liouville semigroup, Banach algebra, <IMG WIDTH="31" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^k}$">-operational calculus, spectrality, spectral operator, quasi-nilpotent
Article copyright: © Copyright 1971 American Mathematical Society