A note on joint capacities in Banach algebras
A note on permanently singular elements in topological algebras
A note on semicharacters
A note on the almost left and almost right joint spectra of R. Harte
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 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 -range and φ- spatial Numerical range of a Tensor
A simple example of a non-commutative Arens product.
A simple and natural example is given of a non-commuting Arens multiplication.
A spectral approach to the Kaplansky problem
A subfield of a complex Banach algebra is not necessarily topologically isomorphic to a subfield of ℂ
A theorem of Gel'fand-Mazur type
Denote by any set of cardinality continuum. It is proved that a Banach algebra A with the property that for every collection there exist α ≠ β ∈ such that is isomorphic to , where , and E is either for some d₀ ∈ ℕ or a 1-dimensional -bimodule with trivial right module action. In particular, ℂ is the unique non-zero prime Banach algebra satisfying the above condition.
A theorem on operator algebras.
Absorbent Sets in Topological Algebras
Adjoining inverses to noncommutative Banach algebras and extensions of operators
Algebra Involutions on the Bidual of a Banach Algebra.
Algebras of functions on mappings.
Algebras of real analytic functions; homorphisms and bounding sets.
In this paper weare interested in subsets of a real Banach space on which different classes of functions are bounded.