Search results for "rete"

A weak comparison principle for solutions of very degenerate elliptic equations

2012

We prove a comparison principle for weak solutions of elliptic quasilinear equations in divergence form whose ellipticity constants degenerate at every point where \(\nabla u\in K\), where \(K\subset \mathbb{R }^N\) is a Borel set containing the origin.

Codimension growth and minimal superalgebras

2003

A celebrated theorem of Kemer (1978) states that any algebra satisfying a polynomial identity over a field of characteristic zero is PI-equivalent to the Grassmann envelope G(A) of a finite dimensional superalgebra A. In this paper, by exploiting the basic properties of the exponent of a PI-algebra proved by Giambruno and Zaicev (1999), we define and classify the minimal superalgebras of a given exponent over a field of characteristic zero. In particular we prove that these algebras can be realized as block-triangular matrix algebras over the base field. The importance of such algebras is readily proved: A is a minimal superalgebra if and only if the ideal of identities of G(A) is a product…

Serial subalgebras of finitary Lie algebras

2000

A Lie subalgebra L of glK(V ) is said to be finitary if it consists of elements of finite rank. We show that, if L acts irreducibly on V , and if V is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of L acts irreducibly on V too. When CharK 6= 2, it follows that the locally solvable radical of such L is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic 6= 2 are hyperabelian.

Non-self-adjoint resolutions of the identity and associated operators

2013

Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $$\{X(\lambda )\}_{\lambda \in {\mathbb R}}$$ , whose adjoints constitute also a resolution of the identity, are studied. In particular, it is shown that a closed operator $$B$$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $$B=\textit{TAT}^{-1}$$ where $$A$$ is self-adjoint and $$T$$ is a bounded inverse.

Existence of a common fixed point for a family of mappings of non‐expansive type on a metric space

1992

Existence of a common fixed point for a family of mappings of non‐expansive type on a metric space with a closure operator is proved.

The p-Laplacian with respect to measures

2013

We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.

Examples of proper k-ball contractive retractions in F-normed spaces

2007

Abstract Assume X is an infinite dimensional F -normed space and let r be a positive number such that the closed ball B r ( X ) of radius r is properly contained in X . The main aim of this paper is to give examples of regular F -normed ideal spaces in which there is a 1-ball or a ( 1 + e ) -ball contractive retraction of B r ( X ) onto its boundary with positive lower Hausdorff measure of noncompactness. The examples are based on the abstract results of the paper, obtained under suitable hypotheses on X .

Fixed point property in Banach lattices with Banach-Saks property

1994

The fixed point property in banach spaces whose characteristic of uniform convexity is less than 2

1993

AbstractWe prove that every Banach space X with characteristic of uniform convexity less than 2 has the fixed point property whenever X satisfies a certain orthogonality condition.

Gleason Parts and Weakly Compact Homomorphismsbetween Uniform Banach Algebras

1999

If points in nontrivial Gleason parts of a uniform Banach algebra have unique representing measures, then the weak and the norm topology coincide on the spectrum. We derive from this several consequences about weakly compact homomorphisms and discuss the case of other uniform Banach algebras arising in complex infinite dimensional analysis.