Among his topics are elements of measure theory, a Hilbert space interlude, linear transformations, locally convex spaces, and

Banach algebras and spectral theory.

To be able to apply methods from the theory of Banach algebras to the solution of those problems, it is essential to determine if a class of linear operators of a sequence space X into itself is a Banach algebra; this is nontrivial if X is a BK space that does not have AK.

infinity]]([LAMBDA])) and (w, w) are Banach algebras.

She covers normed spaces and operators, Frechet spaces and Banach theorems, duality, weak topologies, distributions, the Fourier transform and Sobolev spaces,

Banach algebras, and unbounded operators in a Hilbert space.

Dales, Banach Algebras and Automatic Continuity, London Mathematical Society Monographs, New Series, 24.

Miller, Higher derivations on Banach algebras, Amer.

Remember that a linear function between Banach algebras [phi]: [B.

are Banach algebra isomorphisms, respecting the identities [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and I [d.

Automatic continuity results for linear maps on

Banach algebras, Preprint,1992

This new-in-paperback text is based on lectures given by the author at the advanced undergraduate and graduate levels in Measure Theory, Functional Analysis,

Banach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations.

Russia) presents this text as an introduction to the field, devoting the bulk of it to the classical functional analysis of normed, Banach, and Hilbert spaces, but also covering polynormed spaces and some of their applications, as well as those elements of the theory of

Banach algebras important to the study of spectra.

9) a general square root lemma for

Banach algebras and Banach *-algebras.