Characterizations on 2-isometries

We consider 2-isometries, weak 2-isometries and 2-continuous mappings and investigate the relation between three mappings in linear 2-normed spaces. Also we prove that the Riesz theorem holds when X is a linear 2-normed spaces.     

Surjective L2-isometries on the Projection Lattice

Recently,Gehér and ?emrl have characterized the general form of surjective isometries of the set of all projections on an infinite-dimensional separable Hilbert space using unitaries and antiunitaries.In this paper,we study the surjective L~2-isometries of the projection lattice of an infinite dimensional Hilbert space and show that every such isometry can also be described by unitaries and antiunitaries.     

On subspaces of non-commutative Lp-spaces

We study some structural aspects of the subspaces of the non-commutative (Haagerup) L_p-spaces associated with a general (non-necessarily semi-finite) von Neumann algebra . If a subspace X of contains uniformly the spaces ?_pⁿ, n?1, it contains an almost isometric, almost 1-complemented copy of ?_p. If X contains uniformly the finite dimensional Schatten classes S_pⁿ, it contains their ?_p-direct sum too. We obtain a version of the classical Kadec-Pe?czyński dichotomy theorem for L_p-spaces, p?2. We also give operator space versions of these results. The proofs are based on previous structural results on the ultrapowers of , together with a careful analysis of the elements of an ultrapower which are disjoint from the subspace . These techniques permit to recover a recent result of N. Randrianantoanina concerning a subsequence splitting lemma for the general non-commutative L_p spaces. Various notions of p-equiintegrability are studied (one of which is equivalent to Randrianantoanina's one) and some results obtained by Haagerup, Rosenthal and Sukochev for L_p-spaces based on finite von Neumann algebras concerning subspaces of containing ?_p are extended to the general case.     

关于M1-空间的又一注记

In this note, we prove that, let f be a quasi-open, closed mapping from an M₁-space x onto a q-space (or a space of pointwise countable type) Y, then y is an M₁-space; which partially answers a classic problem. "Is the irreducible closed image of an M₁-space M₁?" (irreducible closed mapping→quasi-open mapping).     

T0-spaces and pointwise convergence

The purpose of this paper is to give several different characterizations of those T₀-spaces E with the property that if F:X × E → Y is separately continuous, then it is jointly continuous. One such is that the lattice 0(E) of open sets of E be a hypercontinuous lattice (i.e. the interval topology on 0(E) is Hausdorff). If E is a sober space, then E must be a quasicontinuous poset endowed with the Scott topology.     

THE CONTRACTION LINEAR METRIC PROJECTIONS IN Lp SPACES

In this paper ,we study the contraction lineartiy for metric projection in Lp spaces,A geometrical property of a subspace Y of Lp is given on which Pr is a contraction projection.     

Maximal theorems of Menchoff-Rademacher type in non-commutative Lq-spaces

Estimates for maximal functions provide the fundamental tool for solving problems on pointwise convergence. This applies in particular for the Menchoff-Rademacher theorem on orthogonal series in L₂[0,1] and for results due independently to Bennett and Maurey-Nahoum on unconditionally convergent series in L₁[0,1]. We prove corresponding maximal inequalities in non-commutative L_q-spaces over a semifinite von Neumann algebra. The appropriate formulation for non-commutative maximal functions originates in Pisier's recent work on non-commutative vector valued L_q-spaces.     

Interpolation between non-commutative BMO and non-commutative Lp-spaces

We prove that for 1?p<q<∞ the analogue of the classical result holds in the setting of a finite von Neumann algebra , equipped with an increasing filtration of von Neumann subalgebras. We also obtain the corresponding results for the real method of interpolation. We discuss the appropriate operator space matrix norms and show that these interpolation results hold in the category of operator spaces.     

On 1-isometries of affine quadrics over finite fields

Letq be a regular quadratic form on a vector space (V, $\mathbb{F}$ ) and assume $4 \leqslant dim V \leqslant \infty \wedge |\mathbb{F}| \in \mathbb{N}$ . A 1-isometry of the central quadric $\mathcal{F}: = \{ x \in V|q(x) = 1\}$ is a permutation ? of $\mathcal{F}$ such that (*) $$q(x - y) = \nu \Leftrightarrow q(x^\varphi - y^\varphi ) = \nu \forall x,y \in \mathcal{F}$$ holds true for a fixed element ν of $\mathbb{F}$ . For arbitraryν ∈ $\mathbb{F}$ we prove that? is induced (in a certain sense) by a semi-linear bijection $(\sigma ,\varrho ):(V,\mathbb{F}) \to (V,\mathbb{F})$ such thatq oσ =? oq, provided $\mathcal{F}$ contains lines and the exceptional case $(\nu = 2 \Lambda |\mathbb{F}| = 3 \Lambda \dim V = 4 \Lambda |\mathcal{F}| = 24)$ is excluded. In the exceptional case and as well in case of dim V = 3 there are counterexamples. The casesν ≠ 2 and v=2 require different techniques.     

Lp-Continuous extreme selectors of multifunctions with decomposable values: Relaxation theorems

Some density theorems of L _p-continuous selectors whose values are extreme points are proved for a class of multivalued maps. applications to the Darboux problem for a differential inclusion are presented.Supported in part by RFFI Grant 93-011-264.     

Bundle convergence of sequences of pairwise uncorrelated operators in von Neumann algebras and vectors in their L2-spaces

Let H be a separable complex Hilbert space, A a von Neumann algebra in ?(H),a faithful, normal state on A. We prove that if a sequence (X_n: n ≥ 1) of uncorrelated operators in A is bundle convergent to some operator X in A and Σ^∞_n=1n⁻² Var(X_n) log²(n + 1) < ∞, then X is proportional to the identity operator on H. We also prove an analogous theorem for certain uncorrelated vectors in the completion L₂=L₂(A,φ) of A given by the Gelfand-Naimark-Segal representation theorem. Both theorems were motivated by a recent one proved by Etemadi and Lenzhen in the classical commutative setting.     

A combinatorial classification of 2-regular simple modules for Nakayama algebras

Enomoto showed for finite dimensional algebras that the classification of exact structures on the category of finitely generated projective modules can be reduced to the classification of 2-regular simple modules. In this article, we give a combinatorial classification of 2-regular simple modules for Nakayama algebras and we use this classification to answer several natural questions such as when there is a unique exact structure on the category of finitely generated projective modules for Nakayama algebras. We also classify 1-regular simple modules, quasi-hereditary Nakayama algebras and Nakayama algebras of global dimension at most two. It turns out that most classes are enumerated by well-known combinatorial sequences, such as Fibonacci, Riordan and Narayana numbers. We first obtain interpretations in terms of the Auslander-Reiten quiver of the algebra using homological algebra, and then apply suitable bijections to relate these to combinatorial statistics on Dyck paths.     

The relation between GTi-spaces and fuzzy proximity spaces, G-compact spaces, fuzzy uniform spaces

In this paper, we study the relation between the fuzzy separation axioms, which had been introduced by the authors in 2001, and the fuzzy proximity defined by Katsaras in 1980. We study also the relation between our fuzzy separation axioms and the G-compactness defined by Gähler in 1995. Moreover, we show here the relation between these fuzzy separation axioms and the fuzzy uniform structures introduced and studied by Gähler and the first author in 1998.     

A classification of 2-complexes with nontrivial self-covers

The main result is the classification of finite regular 2-complexes which have a nontrivial finite-sheeted self-cover. It is shown that a 2-complex K is a member of this class if and only if it may be decomposed as a collection of annuli and circles in the sense made precise in the paper. Intuitively, K is recovered by gluing the boundary components of the annuli to the circles via covering maps.     

Miscellaneous classification results for 2-designs

An orderly algorithm combined with clique searching is used to show that there are—up to isomorphism, in all cases—325,062 resolvable 2-(16,4,2) designs with 339,592 resolutions, 19,072,802 2-(13,6,5) designs, and 15,111,019 2-(14,7,6) designs. Properties of the classified designs are further discussed.