Read e-book online Isometries on Banach spaces: vector-valued function spaces PDF

By Richard J. Fleming, James E. Jamison

ISBN-10: 1420010204

ISBN-13: 9781420010206

ISBN-10: 1584883863

ISBN-13: 9781584883869

A continuation of the authors’ earlier book, Isometries on Banach areas: Vector-valued functionality areas and Operator areas, quantity covers a lot of the paintings that has been performed on characterizing isometries on a number of Banach areas.

Picking up the place the 1st quantity left off, the publication starts off with a bankruptcy at the Banach–Stone estate. The authors contemplate the case the place the isometry is from C 0( Q , X ) to C 0( ok , Y ) in order that the valuables comprises pairs ( X , Y ) of areas. the following bankruptcy examines areas X for which the isometries on LP ( μ , X ) should be defined as a generalization of the shape given by means of Lamperti within the scalar case. The ebook then reviews isometries on direct sums of Banach and Hilbert areas, isometries on areas of matrices with numerous norms, and isometries on Schatten periods. It thus highlights areas on which the crowd of isometries is maximal or minimum. the ultimate bankruptcy addresses extra peripheral subject matters, comparable to adjoint abelian operators and spectral isometries.

Essentially self-contained, this reference explores a primary point of Banach area idea. compatible for either specialists and newbies to the sphere, it bargains many references to supply sturdy assurance of the literature on isometries.

Show description

Read or Download Isometries on Banach spaces: vector-valued function spaces and operator spaces PDF

Best mathematics books

New PDF release: Charming Proofs: A Journey into Elegant Mathematics

Theorems and their proofs lie on the center of arithmetic. In conversing of the only aesthetic traits of theorems and proofs, G. H. Hardy wrote that during appealing proofs 'there is a truly excessive measure of unexpectedness, mixed with inevitability and economy'. fascinating Proofs offers a set of exceptional proofs in user-friendly arithmetic which are tremendously dependent, packed with ingenuity, and succinct.

Complex Cobordism and Stable Homotopy Groups of Spheres - download pdf or read online

Because the book of its first variation, this booklet has served as one of many few on hand at the classical Adams spectral series, and is the easiest account at the Adams-Novikov spectral series. This re-creation has been up to date in lots of areas, in particular the ultimate bankruptcy, which has been thoroughly rewritten with a watch towards destiny study within the box.

Mathematics Past and Present Fourier Integral Operators by V. W. Guillemin (auth.), Jochen Brüning, Victor W. Guillemin PDF

What's the precise mark of suggestion? preferably it might suggest the originality, freshness and exuberance of a brand new leap forward in mathematical notion. The reader will believe this thought in all 4 seminal papers via Duistermaat, Guillemin and Hörmander awarded the following for the 1st time ever in a single quantity.

Extra resources for Isometries on Banach spaces: vector-valued function spaces and operator spaces

Sample text

The space E does have a trivial centralizer since it has no M summands. 11. Example. Let E be the real space previous example. Here we have 1 (2) and define T as in the T ∗ ((1, 1) ◦ ψ1 ) = ψ1 and T ∗ ((−1, 1) ◦ ψ1 ) = −ψ2 and the function ϕ is not well defined. Of course, the centralizer of E is not trivial in this case. There is one last piece of business we would like to attend to before closing this section. 9. The assumption that the space Y is strictly convex enables us to drop the other conditions on the range space N .

If H = hF , then H is a nonzero element of X but T H(t) = V (t)H(ϕ(t)) = 0 for all t ∈ K0 . 2, we conclude that ϕ(K0 ) is dense. If we assume that the nice operator is actually an isometry, we can prove a tiny bit more. 9. Corollary. (i) Suppose that T is an isometry defined from the function module X = (Q, (Xs )s∈Q , X) onto the function module Y = (K, (Yt )t∈K , Y ) where Z(Yt ) is trivial for each t ∈ K such that Yt = {0}. Then there is a function ϕ from K0 = {t ∈ K : Yt = {0}} onto Q0 = {s ∈ Q : Xs = {0}} and a function t → V (t) from K0 into the family of nice operators from Xϕ(t) to Yt such that (10) T F (t) = V (t)F (ϕ(t)) for all t ∈ K0 and F ∈ X.

We want to relax that requirement and consider isometries defined on a closed subspace M of C0 (Q, X). Once again, this parallels the approach taken in Chapter 2. The goal, as always, is to see if we can show that an isometry from such an M onto a subspace N of C0 (K, Y ) is some kind of generalized weighted composition operator. We will see that it is necessary to make some assumptions about the subspace M in order to assure the existence of enough functions of the right kind to make the arguments work.

Download PDF sample

Isometries on Banach spaces: vector-valued function spaces and operator spaces by Richard J. Fleming, James E. Jamison

by Ronald

Rated 4.96 of 5 – based on 41 votes