Nonstandard Ideals, Unicellularity, and Algebras Associated with a Shift Operator

  • N. K. Nikol’skii
Part of the Seminars in Mathematics book series (SM)


The shift operator in sequence spaces, its invariant subspaces, and applications of the latter have formed the topic of a host of papers, beginning with the earliest studies of Shilov [1], Beurling [2], and Donoghue [3] and extending up to the fundamental monographs [4, 5] and other recently published works [6–17], which we shall presently discuss in further detail. As the title of our article suggests, we propose to amplify on the problem (see [8, 10, 11]) of the unicellularity of the weighted shift operators and its algebraic treatment. Many of the propositions proved below have been announced in [11] or the shorter communication [18], and some others are contained in [9] as well.


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© Springer Science+Business Media New York 1972

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  • N. K. Nikol’skii

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