Rota-Baxter operators appeared in the work of Baxter  on differential operators on commutative Banach algebras
, being particularly useful in relation to the Spitzer identity.
The topics include generalization of C*-algebra methods via real positivity for operator and Banach algebras
, higher weak derivatives and reflexive algebras of operators, spectral multiplicity and odd K-theory-II, the topology of natural numbers and entropy of arithmetic functions, Hochschild cohomology for tensor products of factors, and the structure and applications of real C*-algebras.
Lashkarizadeh Bami, The multiplier algebra and BSE property of the direct sum of Banach algebras
By the middle of the summer of 1958 I finished writing my Diploma thesis: a theorem of decomposition of an anti-symmetric Banach algebra
into a direct sum of two symmetric Banach algebras
which Foias and myself proved.
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.
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.
Remember that a linear function between Banach algebras
Automatic continuity results for linear maps on Banach algebras
Twenty five years ago Johnson, Kadison, and Ringrose initiated the study of cohomology in Banach algebras
and operator algebras in a series of papers [13,14,15,16,17].