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- W2001237046 abstract "Let Y be a closed subspace of Lp(μ), where μ is an arbitrary measure and 1 < p < ∞. It is shown that every invertible operator V on Y such that sup{¦|Vn¦|: n = 0, ±1, ±2,…} < ∞ (in particular, every surjective isometry of Y) can be expressed in the form V = eiA, where A is well bounded of type (B) (i.e., A has a spectral “diagonalization” analogous to, though weaker than, that in the spectral theorem for self-adjoint operators). This result, which fails if Y is replaced by an arbitrary reflexive space, is obtained by a blend of the transference method of Coifman and Weiss with Stečkin's Theorem and a recent result in abstract operator theory. It has the direct consequence that every uniformly bounded one-parameter group on Y is the Fourier-Stieltjes transform of a projection-valued mapping of R. An additional consequence is that every hermitian-equivalent operator on Y is well bounded of type (B). In the setting of an arbitrary Banach space X, power-bounded operators with a logarithm of the form iA with A well bounded of type (B) are studied. It is shown that if U is such an operator on X, then for every function f of bounded variation on the unit circle, ∑n = − ∞∞ ̂tf(n) Un converges in the strong operator topology. This result, which formally is a transference by U of Stečkin's Theorem, makes it possible to calculate directly from U a (normalized) logarithm for U and the spectral projections for the logarithm." @default.
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- W2001237046 date "1987-01-01" @default.
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- W2001237046 title "Stečkin's Theorem, transference, and spectral decompositions" @default.
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- W2001237046 doi "https://doi.org/10.1016/0022-1236(87)90128-5" @default.
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