A note on a class of Banach algebra-valued polynomials.
A note on a construction of J. F. Feinstein
In [6] J. F. Feinstein constructed a compact plane set X such that R(X), the uniform closure of the algebra of rational functions with poles off X, has no non-zero, bounded point derivations but is not weakly amenable. In the same paper he gave an example of a separable uniform algebra A such that every point in the character space of A is a peak point but A is not weakly amenable. We show that it is possible to modify the construction in order to produce examples which are also regular.
A note on criteria of Le Page and Hirschfeld-Żelazko for the commutativity of Banach algebras
A note on distribution spaces on manifolds.
A note on joint capacities in Banach algebras
A note on permanently singular elements in topological algebras
A note on regular elements in Calkin algebras.
An element a of the Banach algebra A is said to be regular provided there is an element b belonging to A such that a = aba. In this note we study the set of regular elements in the Calkin algebra C(X) over an infinite-dimensional complex Banach space X.
A note on semicharacters
A note on the almost left and almost right joint spectra of R. Harte
A Note on the Bidual of a JB-Algebra.
A note on the continuity of multilinear mappings in topological modules.
A note on the differences of the consecutive powers of operators
We present two examples. One of an operator T such that is precompact in the operator norm and the spectrum of T on the unit circle consists of an infinite number of points accumulating at 1, and the other of an operator T such that is convergent to zero but T is not power bounded.
A note on the joint spectrum in commutative Banach algebras
A Note on the Raical of a Banach Algebra.
A note on the singular spectrum.
We compare the singular spectrum of a Banach algebra element with the usual spectrum and exponential spectrum.
A note on the spectral mapping theorem
A note on topologically nilpotent Banach algebras
A Banach algebra A is said to be topologically nilpotent if tends to 0 as n → ∞. We continue the study of topologically nilpotent algebras which was started in [2]
A properly infinite Banach *-algebra with a non-zero, bounded trace
A properly infinite C*-algebra has no non-zero traces. We construct properly infinite Banach *-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly "close" to the class of C*-algebras, in the sense that they can be hermitian or *-semisimple.
A property for locally convex *-algebras related to property (T) and character amenability
For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that has property (FH) if and only if G has property (T). On...
A -range and φ- spatial Numerical range of a Tensor