Search results for "rete"

Varieties of almost polynomial growth: classifying their subvarieties

2007

Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).

Matrix algebras of polynomial codimension growth

2007

We study associative algebras with unity of polynomial codimension growth. For any fixed degree $k$ we construct associative algebras whose codimension sequence has the largest and the smallest possible polynomial growth of degree $k$. We also explicitly describe the identities and the exponential generating functions of these algebras.

On a normal form of symmetric maps of [0, 1]

1980

A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.

Linearization of holomorphic mappings on fully nuclear spaces with a basis

1994

In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

The Riesz Representation Theorem and Extension of Vector Valued Additive Measures

2001

Weakly uniformly continuous holomorphic functions and the approximation property

2001

Abstract We study the approximation property for spaces of Frechet and Gâteaux holomorphic functions which are weakly uniformly continuous on bounded sets. We show when U is a balanced open subset of a Baire or barrelled metrizable locally convex space, E , that the space of holomorphic functions which are weakly uniformly continuous on U -bounded sets has the approximation property if and only if the strong dual of E , E ′ b , has the approximation property. We also characterise the approximation property for these spaces of vector-valued holomorphic functions in terms of the tensor product of the corresponding space of scalar-valued holomorphic functions and the range space.

Geometric properties of involutive distributions on graded manifolds

1997

AbstractA proof of the relative version of Frobenius theorem for a graded submersion, which includes a very short proof of the standard graded Frobenius theorem is given. Involutive distributions are then used to characterize split graded manifolds over an orientable base, and split graded manifolds whose Batchelor bundle has a trivial direct summand. Applications to graded Lie groups are given.

The spectra of some algebras of analytic mappings

1999

Abstract Let E be a Banach space with the approximation property and let F be a Banach algebra with identity. We study the spectrum of the algebra H b(E, F) of all holomorphic mappings f : E → F that are bounded on the bounded subsets of E.

A characterization of the Schur property through the disk algebra

2017

[EN] In this paper we give a new characterization of when a Banach space E has the Schur property in terms of the disk algebra. We prove that E has the Schur property if and only if A(D, E) = A(D,E-w). (C) 2016 Elsevier Inc. All rights reserved.

A note on strongly Lie nilpotency

1991

In this note the authors studies strongly Lie nilpotent rings and proves that if a ringR is strongly Lie nilpotent thenR(2), the ideal generated by all commutators, is nilpotent.