On Some Properties of Segal Algebras and Their Multipliers.
On some von Neumann topological algebras.
On spectral continuity of positive elements
Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the...
On spectral homomorphisms and continuous functions of Banach algebra elements
On splitting of extensions of rings and topological rings.
On strongly closed subalgebras of B(X)
On Tensor Products of Banach Lattices.
On the abstract theorem of Picard.
On the algebra of smooth operators
Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra L(s',s) of so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s) and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN) of s.
On the Arens products and reflexive Banach algebras.
On the Barrelledness of a topological Algebra Relative to its Spectrum
On the Beurling algebras -derivations and extensions.
On the categories and . II
On the Cauchy functional inequality in Banach modules.
On the circle-exponent function
On the closure of modules of continuously differentiable mappings
On the contracted -algebra of a polycyclic monoid.
On the differences of the consecutive powers of Banach algebra elements
Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of and .
On the Facial Structure of the Unit Ball of a GM-Space.
On the fundamental inequality in locally multiplicatively convex algebras