A solution of one Problem of Lindenstrauss and Rosenthal on Subspace Homogeneous and Quotient Homogeneous Banach Spaces with Application to the Approximation Problem and to the Schroeder - Bernstein Problem

In article is constructed a wide couple of pairwice non-isomorphic separable superreflexive Banach spaces E that are subspace homogeneous. Their conjugates are quotient homogeneous. None of this couple neither isomorphic to its Cartesian square nor has the approximation property. At the same time, any such E is isomorphic to E+ E+ W for some Banach space W and, hence, solves the Schroeder - Bernstein problem.Comment: Latex2

On Banach spaces with the Tsirelson property

A Banach space X is said to have the Tsirelson property if it does not contain subspaces that are isomorphic to l_{p}, p in [1,infty) or c_{0}. The article contains a quite simple method to producing Banach spaces with the Tsirelson property.Comment: Latex2

An example of a Banach Space with a Subsymmetric Basis, which has the Hereditarily Approximation Property

W.B. Johnson has constructed a series of Banach spaces non isomorphic to the Hilbert one that have the hereditarily approximation property (shortly hereditarily AP): all their subspaces also have the AP. All these examples were ''sufficiently'' non-symmetric and this fact allows Johnson to ask: whether there exists any Banach space $X$ with symmetric (or, at least, subsymmetric) basis, distinct from the Hilbert space such that each its subspace has the AP? In this paper is shown that there is a Banach space with a subsymmetric basis (non-equivalent to any symmetric one), which enjoys the hereditarily AP.Comment: Latex2e, revised versio

On Extension of Operators in Classes of Finitely Equivalent Banach Spaces. Part 2

In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banach space $X$. Both problems are considered in two variants: isometric and isomorphic ones. Received a full solution of the first problem and the solution, close to final one for the second problem.Comment: Latex2e, This paper is a continuation of the first par

A solution of one J. Bourgain's problem

It is proved that there exists a separable reflexive Banach space W that contains an isomorphic image of every separable superreflexive Banach space. This gives the affirmative answer on one J. Bourgain's questionComment: Latex2e, the third, revised versio

On sub B-convex Banach spaces

In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any separable sub B-convex Banach space X may be almost isometrically embedded in a separable Banach space G(X) of the same cotype as X, which has a series of properties. Namely, G(X) is an approximate envelope, i.e. any separable Banach space which is finitely representable in G(X) may be almost isometrically embedded into G(X); G(X)is almost isotropic; G(X) is existentially closed in a class of all spaces that are finitely equivalent to it; the conjugate space to G(X) is of cotype 2; every operator from its conjugate into the Hilbert space is absolutely summing; every projection P in G(X) of finite rank has a norm that infinitely growth with the dimension of its range. If, in addition, X is of cotype 2, then G(X) has more impressive properties: every operator from G(X) into the Hilbert space is absolutely summing; the injective and projective tensor products of G(X) by itself are identical.Comment: Latex2

On algebraic properties of sets of Banach ideal function spaces

It is shown that every set I(m) of Banach lattices of measurable functions defined on a measure space (Q,S,m), equipped with a some natural ordering became a modular lattice, which is Dedekind complete provided m is a probability measure. Moreover, some natural operations on considered spaces are in Galois connexion.Comment: Latex2e, corrected versio

Asymptotic properties of high-pT particle production in hadron-hadron, hadron-nucleus and nucleus-nucleus collisions at high energies

The concept of z-scaling reflecting the general features of particle substructure, constituent interaction and mechanism of particle formation is reviewed. Experimental data on the cross sections obtained at ISR, SpS and Tevatron are used in the analysis. The properties of data z-presentation, the energy and angular independencies, the power law, A- and F-dependencies, are discussed. The use of z-scaling to search for new physics phenomena in hadron-hadron, hadron-nucleus and nucleus-nucleus collisions is suggested. The violation of z-scaling characterized by the change of the fractal dimension is considered as a new and complimentary signature of nuclear phase transition.Comment: 21 pages, LaTeX, 36 figures, Invited talk presented at the 6th International Workshop "Relativistic Nuclear Physics: from Hundreds of MeV to TeV", Varna, Bulgaria, September 10-16, 200

Z-scaling from tens of GeV to TeV

The concept of z-scaling reflecting the general features of internal particle substructure, constituent interaction and mechanism of particle formation at high-pT is reviewed. Experimental data on inclusive cross sections obtained at U70, ISR, SpS, RHIC and Tevatron are used in the analysis. The properties of data z-presentation such as the energy independence, power law and A-dependence are discussed. The properties of z-scaling are argued to be connected with the fundamental symmetries such as self-similarity, locality and fractality. The use of z-scaling to search for new physics phenomena in hadron-hadron and hadron-nucleus collisions is suggested. RHIC data used in our new analysis confirm z-scaling in pp collisions. High-pT particle spectra at LHC energies are predicted. Violation of z-scaling characterized by the change of anomalous fractal dimension is considered as a new and complementary signature of new physics phenomena.Comment: 18 pages, LaTeX, 24 figures, Invited talk presented at the 7th International Workshop "Relativistic Nuclear Physics: from Hundreds of MeV to TeV", Stara Lesna, Slovak Republic, August 25-30, 200

Self-similarity of negative particle production from the Beam Energy Scan Program at STAR

We present the spectra of negative charged particle production in Au+Au collisions from STAR for the first phase of the RHIC Beam Energy Scan Program measured over a wide range of collision energy sqrt s{NN}=7.7-200 GeV, and transverse momentum of produced particle in different centralities at |eta|<0.5. The spectra demonstrate strong dependence on collision energy which enhances with pT. An indication of self-similarity of negative charged particle production in Au+Au collisions is found. The constituent energy loss as a function of energy and centrality of collisions and transverse momentum of inclusive particle was estimated in the $z$-scaling approach. The energy dependence of the model parameters - the fractal and fragmentation dimensions and "specific heat", was studied.Comment: 13 pages, LaTeX, 16 figures, Presented at the International Conference "HADRON STRUCTURE'15", 29 June -- 3 July, 2015, Horny Smokovec, Slovak Republic. Preprint JINR E1-2015-8