Search results for "Linear"
showing 10 items of 7165 documents
Linear quotients of Artinian Weak Lefschetz algebras
2013
Abstract We study the Hilbert function and the graded Betti numbers for “generic” linear quotients of Artinian standard graded algebras, especially in the case of Weak Lefschetz algebras. Moreover, we investigate a particular property of Weak Lefschetz algebras, the Betti Weak Lefschetz Property, which makes possible to completely determine the graded Betti numbers of a generic linear quotient of such 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].
*-Representations, seminorms and structure properties of normed quasi*-algebras
2008
The class of -representations of a normed quasi -algebra (X;A0) is in- vestigated, mainly for its relationship with the structure of (X;A0). The starting point of this analysis is the construction of GNS-like -representations of a quasi -algebra (X;A0) dened by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms denes some seminorms (in some cases, C -seminorms) that provide useful information on the structure of (X;A0) and on the continuity properties of its -representations. 1. Introduction. A quasi -algebra is a couple (X;A0), where X is a vector space with involution , A0 is a -algebra and a vector subspace of X, and X is an A0-bimodule who…
Farkas-Minkowski systems in semi-infinite programming
1981
The Farkas-Minkowski systems are characterized through a convex cone associated to the system, and some sufficient conditions are given that guarantee the mentioned property. The role of such systems in semi-infinite programming is studied in the linear case by means of the duality, and, in the nonlinear case, in connection with optimality conditions. In the last case the property appears as a constraint qualification.
New Results on Identifiability of Nonlinear Systems
2004
Abstract In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability. In a previous paper (Busvelle and Gauthier, 2003), we have established that • If the number of observations is three or more, then, systems are generically identifiable. • If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results i…
On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces
2007
We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak ∗ separable admits a closed linear subspace whose dual is not weak ∗ -separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2homogeneous polynomials.
On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials
2007
Given an operator ideal I, we study the multi-ideal I ο L and the polynomial ideal I ο P). The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained.
Existence of Unconditional Bases in Spaces of Polynomials and Holomorphic Functions
2002
Our main result shows that every Montel Kothe echelon or coechelon space E of order 1 < p ≤ ∞ is nuclear if and only if for every (some) m ≥ 2 the space ((mE), τ0) of m-homegeneus polynomials on E endowed with the compact-open topology τ0 has an unconditional basis if and only if the space (ℋ(E), τδ) of holomorphic functions on E endowed with the bornological topology τδ associated to τ0 has an unconditional basis (for coechelon spaces τδ equals τ0). The main idea is to extend the concept of the Gordon-Lewis property from Banach to Frechet and (DF) spaces. In this way we obtain techniques which are used to characterize the existence of unconditional basis in spaces of m-th (symmetric) tenso…
Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one
2016
This paper provides various “contractivity” results for linear operators of the form I−C where C are positive contractions on real ordered Banach spaces X. If A generates a positive contraction semigroup in Lebesgue spaces Lp(μ), we show (M. Pierre's result) that A(λ−A)−1 is a “contraction on the positive cone”, i.e. A(λ−A)−1x≤x for all x∈L+p(μ)(λ>0), provided that p⩾2. We show also that this result is not true for 1 ⩽ p<2. We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone X+. We deduce from this result that, in such spaces, I−C is a contraction on X+ for any positive projection…