Analytic properties in the spectrum of certain Banach algebras

We show a sufficient condition for a domain in to be a H ^∞-domain of holomorphy. Furthermore if a domain has the Gleason property at a point and the projection of the n − 1th order generalized Shilov boundary does not coincide with Ω then is schlicht. We also give two examples of pseudoconvex domains in which the spectrum is non-schlicht and satisfy several other interesting properties.      

Construction of the syzygy module in automaton monomial algebras

In this paper, we consider the problem of algorithmically constructing the left syzygy module for a finite system of elements in an automaton monomial algebra. The class of automaton monomial algebras includes free associative algebras and finitely presented algebras. In such algebras the left syzygy module for a finite system of elements is finitely generated. In general, the left syzygy module in an automaton monomial algebra is not finitely generated. Nevertheless, the generators of the left syzygy module have a recursive specification with the help of regular sets. This allows one to solve many algorithmic problems in automaton monomial algebras. For example, one can solve linear equations, recognize the membership in a left ideal, and recognize zero-divisors. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 101–113, 2005.     

Pseudo-amenability of certain semigroup algebras

In this paper, we investigate the pseudo-amenability of semigroup algebra ? ¹(S), where S is an inverse semigroup with uniformly locally finite idempotent set. In particular, we show that for a Brandt semigroup \(S={\mathcal{M}}^{0}(G,I)\), the pseudo-amenability of ? ¹(S) is equivalent to the amenability of G.     

Quasi-identities of certain finite algebras

In this note an example of a finite lattice not having a finite basis of quasiidentities and an analogous example for algebras of the type <1, 1> are indicated. Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 335–338, September, 1977.     

Forms of certain hopf algebras

Let Ψ be a field, G a finite group of automorphisms of Ψ, and Φ the fixed field of G. Let H be a Hopf algebra over Ψ. For g ∈ G we define a Hopf algebra H_g which has the same underlying vector space as H and modified operations and show that the tensor product (over Ψ) ?_{g ∈ G} H_g has a Φ-form. As a consequence we see that if n>0 is an integer and Φ is a field of characteristic zero or p>0 with (n,p)=1, then there is a finite dimensional Hopf algebra over Φ with antipode of order 2n.     

Isometries of certain operator algebras

To a given basis on an -dimensional Hilbert space , we associate the algebra of all linear operators on having every as an eigenvector. So, is commutative, semisimple, and -dimensional. Given two algebras of this type, and , there is a natural algebraic isomorphism of and . We study the question: When does preserve the operator norm?

     

On certain properties of the relative entropy of states of operator algebras

On leave of absence from the Mathematical Institute HAS, Budapest. This research was partially supported by the Hungarian National Foundation for Scientific Research grant No. 1171     

Limit distributions of certain characteristics of random automaton graphs

The paper deals with the following characteristics of random automaton graphs: the numbers of recurrent and nonrecurrent vertices, the number and dimensions of the components of strong connectivity, and the number of vertices attainable from a given one. Limit theorems are found for the distributions of these characteristics.Translated from Matematicheskie Zametki, Vol. 14, No. 1, pp. 133–141, July, 1973.In conclusion, the author wishes to express his gratitude to V. E. Stepanov for his direction and help with this paper.     

Generalized Clifford algebras and certain infinite dimensional Lie algebras

The embedding of certain infinite dimensional Lie algebras in generalized Clifford algobras C(N, p) is given. The correspondence between C(N,2) andgl(N, C) asN⇌∞ is pointed out.     

Homomorphisms of certain Banach function algebras

In this note, we study homomorphisms with domainD ⁿ(X) orLipα(X, d) of which ranges are certain Banach function algebras and determine in which cases these homomorphisms are compact.     

Lie derivations of certain CSL algebras

It is shown that each Lie derivation on a reflexive algebra, whose lattice is completely distributive and commutative, can be uniquely decomposed into the sum of a derivation and a linear mapping with image in the center of the algebra. Supported by NNSFC (No. 10571054) and a grant (No.04KJB110116) from the government of Jiangsu Province of China.