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
On the generalized Drazin inverse and generalized resolvent
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel....
On the ideal structure of algebras of LMC-algebra valued functions
Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.
On the ideals of extended quasi-nilpotent Banach algebras.
On the joint spectral radii of commuting Banach algebra elements
Some inequalities are proved between the geometric joint spectral radius (cf. [3]) and the joint spectral radius as defined in [7] of finite commuting families of Banach algebra elements.
On the joint spectral radius
We prove the -spectral radius formula for n-tuples of commuting Banach algebra elements
On the Kleinecke-Shirokov Theorem for families of derivations
It is proved that Riesz elements in the intersection of the kernel and the closure of the image of a family of derivations on a Banach algebra are quasinilpotent. Some related results are obtained.
On the largest generalized joint spectrum
On the Lebesgue decomposition of the normal states of a JBW-algebra
In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.
On the left and right joint spectra in Banach algebras
On the locally -convex algebra and a differential-geometric interpretation of it.
On the projectivity and flatness of some group modules
In the sequel of the work of H. G. Dales and M. E. Polyakov we give a few more examples of modules over the Banach algebra L¹(G) whose projectivity resp. flatness implies the compactness resp. amenability of the locally compact group G.
On the punctured neighbourhood theorem.