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- W4253050006 abstract "The purpose of this paper is to call attention to some interesting weakly closed algebras related to a bounded linear operator $T$ acting on a Banach space $mathfrak {X}$ and their associated lattices of invariant subspaces, namely, the algebras generated by the polynomials and by the rational functions in $T$, and the commutant and the double-commutant of $T$. The relationship between those algebras and their lattices, as well as the ones corresponding to the operators induced by $T$ on an invariant subspace (restriction), or on the quotient space $mathfrak {X}/mathfrak {M}$ (where $mathfrak {M}$ is an invariant subspace of a given type) are analyzed. Several results relative to the decomposition of invariant subspaces and the topological structure of the lattices (under the âgap-between-subspacesâ metric topology) are also considered." @default.
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- W4253050006 date "1972-11-01" @default.
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- W4253050006 title "Analytically Invariant and Bi-Invariant Subspaces" @default.
- W4253050006 doi "https://doi.org/10.2307/1996265" @default.
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