Characterization Of Subspaces Research Articles

Toward an intuitive understanding of the structure of near-vector spaces

In this article we analyze the definition André proposed for near-vector spaces to make it more transparent. We also study the class of near-vector spaces over division rings and give a characterization of regularity that gives a new insight into the decomposition of near-vector spaces into regular subspaces. We explicitly describe span and deduce a new characterization of subspaces.

The uniqueness of the best non-symmetric $L_1$-approximant with a weight for continuous functions with values in KB-space

We investigate the problem of uniqueness of the best non-symmetrical $L_1$-approximant with a weight for continuous functions on metric compact set $Q$ with values in strictly convex partially ordered KB-space $X$ by subspaces of space $C(Q, X)$ of continuous functions on $Q$ with values in $X$. We obtain the characterization of subspaces of uniqueness of the best $(\alpha, \beta)$-approximant in integral metric with a weight for functions of space $C(Q, X)$ in terms of classes of "test" functions.

On Subspaces of Cesàro Spaces

We obtain a characterization of subspaces of L p , with 1 < p < ∞, on which the L p -norm is equivalent to the norm of the Cesaro space Ces p . Also, we show that Ces p has a complemented copy of the Cesaro sequence space ces p .

Basis adaptation in homogeneous chaos spaces

We present a new method for the characterization of subspaces associated with low-dimensional quantities of interest (QoI). The probability density function of these QoI is found to be concentrated...

Lattices generated by orbits of subspaces under finite singular orthogonal groups I

Let F q ( 2 ν + δ + l ) be the ( 2 ν + δ + l ) -dimensional vector space over the finite field F q . In the paper we assume that F q is a finite field of odd characteristic, and O 2 ν + δ + l , Δ ( F q ) the singular orthogonal groups of degree 2 ν + δ + l over F q . Let M be any orbit of subspaces under O 2 ν + δ + l , Δ ( F q ) . Denote by L the set of subspaces which are intersections of subspaces in M and the intersection of the empty set of subspaces of F q ( 2 ν + δ + l ) is assumed to be F q ( 2 ν + δ + l ) . By ordering L by ordinary or reverse inclusion, two lattices are obtained. This paper studies the inclusion relations between different lattices, a characterization of subspaces contained in a given lattice L , and the characteristic polynomial of L .

Lattices generated by orbits of subspaces under finite singular pseudo-symplectic groups I

Let F q ( 2 ν + 1 + l ) be the ( 2 ν + 1 + l ) -dimensional vector space over the finite field F q . In the paper we assume that F q is a finite field of characteristic 2, and Ps 2 ν + 1 + l , 2 ν + 1 ( F q ) the singular pseudo-symplectic groups of degree 2 ν + 1 + l over F q . Let M be any orbit of subspaces under Ps 2 ν + 1 + l , 2 ν + 1 ( F q ) . Denote by L the set of subspaces which are intersections of subspaces in M and the intersection of the empty set of subspaces of F q ( 2 ν + 1 + l ) is assumed to be F q ( 2 ν + 1 + l ) . By ordering L by ordinary or reverse inclusion, two lattices are obtained. This paper studies the inclusion relations between different lattices, a characterization of subspaces contained in a given lattice L , and the characteristic polynomial of L .

Problem of uniqueness of an element of the best nonsymmetric L 1-approximation of continuous functions with values in KB-spaces

We consider the problem of characterization of subspaces of uniqueness of an element of the best nonsymmetric L 1-approximation of functions that are continuous on a metric compact set of functions with values in a KB-space. We find classes of test functions that characterize the uniqueness of an element of the best nonsymmetric approximation.

A characterization of subspaces and quotients of reflexive banach spaces with unconditional bases

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property (UTP) has the UTP. This is used to prove that a separable reflexive Banach space with the UTP embeds into a reflexive Banach space with an unconditional basis. This solves several longstanding open problems. In particular, it yields that a quotient of a reflexive Banach space with an unconditional finite-dimensional decomposition (UFDD) embeds into a reflexive Banach space with an unconditional basis

Lattices generated by orbits of subspaces under finite singular unitary group and its characteristic polynomials

Let F q 2 (n+l) be the ( n+ l)-dimensional vector space over the finite field F q 2 , and U n+l,n( F q 2 ) the singular Unitary groups of degree n+ l over F q 2 . Let M be any orbit of subspaces under U n+l,n( F q 2 ) . Denote by L the set of subspaces which are intersections of subspaces in M , where the intersection of the empty set of subspaces of F q 2 (n+l) is assumed to be F q 2 (n+l) . By ordering L by ordinary or reverse inclusion, two lattices are obtained. This paper studies the inclusion relations between different lattices, a characterization of subspaces contained in a given lattice L , when the lattices form a geometric lattice, and the characteristic polynomial of L .

Lattices Generated by Orbits of Subspaces Under Finite Singular Classical Groups and Its Characteristic Polynomials

Let be the (2ν + l)-dimensional vector space over the finite field 𝔽 q , and Sp 2ν+l,ν(𝔽 q ) the singular symplectic groups of degree 2ν + l over 𝔽 q . Let ℳ be any orbit of subspaces under Sp 2ν+l,ν(𝔽 q ). Denote by ℒ the set of subspaces which are intersections of subspaces in ℳ and the intersection of the empty set of subspaces of is assumed to be . By ordering ℒ by ordinary or reverse inclusion, two lattices are obtained. This paper studies the inclusion relations between different lattices, a characterization of subspaces contained in a given lattice ℒ, when the lattices form geometric lattice, and the characteristic polynomial of ℒ.

The slice map problem and approximation properties

We show that a σ-weakly closed subspace J of the bounded operators B H on an infinite dimensional Hilbert space H has Property S σ (the Fubini product (LT)=L ⊗ for all σ-weakly closed subspaces T ⊂B( H )) if and only if J satisfies a certain approximation property, which we call the σ-weak approximation property. The σ-weak approximation property is implied by (but does not imply) the (weak- ∗) completely bounded approximation property. Moreover, if J has the σ-weak approximation property, then the predual J ∗ has the approximation property for Banach spaces. We also prove analagous results for Property S (and variations of Property S) for C ∗-algebras. As an application of our characterization of subspaces with Property S σ , we show that the reflexive algebra tensor product formula alg L 1 ⊗ alg L 2 = alg( L 1 ⊗ L 2) is not always valid. In fact, we show that for each of the types II 1, II ∞, and III λ (0 ⩽ λ ⩽ 1), there is a separably acting factor M = alg L 1 of that type and a reflexive algebra A = alg L 2 such that alg L 1 ⊗ alg L 2 is strictly contained in alg( L 1 ⊗ L 2).

On the characterization of subspaces and quotient spaces of stable power series spaces of finite type

On the characterization of subspaces and quotient spaces of stable power series spaces of finite type

Characterizations of subspaces, quotients and subspaces of quotients of Lp

Characterizations of subspaces, quotients and subspaces of quotients of Lp

Characterization of subspaces of certain sequence spaces

Characterization of subspaces of certain sequence spaces

A Characterization of Subspaces X of l p for which K(X) is an M- Ideal in L(X)

A Characterization of Subspaces X of l p for which K(X) is an M- Ideal in L(X)

A characterization of subspaces $X$ of $l\sb p$ for which $K(X)$ is an $M$-ideal in $L(X)$

A characterization of subspaces $X$ of $l\sb p$ for which $K(X)$ is an $M$-ideal in $L(X)$

A series characterization of subspaces of 𝐿_{𝑝}(𝜇) spaces

A series characterization of subspaces of 𝐿_{𝑝}(𝜇) spaces

Sur un théorème de J. L. Krivine concernant la caracterisation des classes d’espaces isomorphes a des espaces d’orlicz généralisés et des classes voisines

The classL p the classes λ-SL p of spaces λ isomorphic to subspaces ofL p spaces and λ-QL p of subquotients have been characterized in the literature by formulas of certain simple forms. A theorem of Krivine gives a general demonstration of these results in the framework of ψ normed spaces. In particular, characterizations of subspaces and subquotients of certain classes of generalized Orlicz spaces are obtained.

A characterization of subspaces of $L^{p}(μ)$

A characterization of subspaces of $L^{p}(μ)$