Continuation of a linear operator to an involution operator

A bounded linear operatorA:X→X in a linear topological spaceX is called ap-involution operator,p≥2, ifA ^p=I, whereI is the identity operator. In this paper, we describe linearp-involution operators in a linear topological space over the field ℂ and prove that linear operators can be continued to involution operators. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 671–676, May, 1997. Translated by M. A. Shishkova     

Intuitionistic <Emphasis Type="Italic">I</Emphasis>-fuzzy topological spaces

The main purpose of this paper is to introduce the concept of intuitionistic I-fuzzy quasi-coincident neighborhood systems of intuitiostic fuzzy points. The relation between the category of intuitionistic I-fuzzy topological spaces and the category of intuitionistic I-fuzzy quasi-coincident neighborhood spaces are studied. By using fuzzifying topology, the notion of generated intuitionistic I-fuzzy topology is proposed, and the connections among generated intuitionistic I-fuzzy topological spaces, fuzzifying topological spaces and I-fuzzy topological spaces are discussed. Finally, the properties of the operators Iω, ι are obtained.     

Complex symplectic geometry with applications to ordinary differential operators

Complex symplectic spaces, and their Lagrangian subspaces, are defined in accord with motivations from Lagrangian classical dynamics and from linear ordinary differential operators; and then their basic algebraic properties are established. After these purely algebraic developments, an Appendix presents a related new result on the theory of self-adjoint operators in Hilbert spaces, and this provides an important application of the principal theorems.

     

Perturbation Analysis of Moore–Penrose Quasi-linear Projection Generalized Inverse of Closed Linear Operators in Banach Spaces

In this paper, we investigate the perturbation problem for the Moore–Penrose bounded quasi-linear projection generalized inverses of a closed linear operaters in Banach space. By the method of the perturbation analysis of bounded quasi-linear operators, we obtain an explicit perturbation theorem and error estimates for the Moore–Penrose bounded quasi-linear generalized inverse of closed linear operator under the T-bounded perturbation, which not only extend some known results on the perturbation of the oblique projection generalized inverse of closed linear operators, but also extend some known results on the perturbation of the Moore–Penrose metric generalized inverse of bounded linear operators in Banach spaces.     

The topological structure of a certain Menger space

In this paper we will reconsider the topological structure of Menger probabilistic normed spaces (briefly PN-spaces) under the t-norm M. We will prove that this topology is compatible with the topology induced by a countable and separating family of semi-norms, and hence the well-known theorems of classical functional analysis (such as the principle of uniform boundedness, open mapping and closed graph theorems) are valid in this context also. We will meanwhile obtain a method by which one may construct easily a large class of PN-spaces. Finally, using this method, we see that a certain subspace of bounded linear operators between PN-spaces, i.e. the class of strongly bounded linear operators, has a natural PN structure.     

Diagonal multilinear operators on Köthe sequence spaces

We analyse the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated Köthe sequence spaces. We establish relationships with spaces of multipliers and apply these results to describe diagonal multilinear operators from Lorentz sequence spaces. We also define and study some properties of the ideal of (E, p)-summing multilinear mappings, a natural extension of the linear ideal of absolutely (E, p)-summing operators.     

On -topological vector spaces generated by a co-tower of L-topological vector spaces

In this paper, a characterization for an I(L)-topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I(L)-topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I(L)-topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I(L)-topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too.     

Generalized difference sequence spaces on seminormed space defined by Orlicz functions

In this paper we define the sequence space ℓ _M (Δ ^m , p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving ℓ _M (Δ ^m , p, q, s).      

关于Lipschitz映射空间的可余子空间

该文研究Lipschitz映射空间作为一个Banach空间的结构性质，主要研究了它的闭子空间有界线性算子空间（赋予算子范数）在其中的可余性．     

Spektraltheorie verwandter operationen

This is a résumé of A. Pietsch’s concept of related linear operators in the study of spectral properties and homomorphism theorems forp-bounded linear operators on Mackey-complete topological vector spaces. It turns out that many results proved by various authors in the setting of Mackey-complete topological vector spaces follow directly from the corresponding classical results by means of purely algebraic relations.     

N-邻域与N-Fuzzy有界集

本文研究了Fuzzy拓扑空间中的N-邻域与N-Fuzzy有界集问题.利用N-邻域引入N-Fuzzy有界集概念,讨论了其与另两种Fuzzy有界集的关系,获得了三种Fuzzy有界集的等价刻画及N-Fuzzy有界集的一些基本性质,推广了Fuzzy有界集的已有结果.     

Separation and Epimorphisms in Quasi-Uniform Spaces

We study some categorical aspects of quasi-uniform spaces (mainly separation and epimorphisms) via closure operators in the sense of Dikranjan, Giuli, and Tholen. In order to exploit better the corresponding properties known for topological spaces we describe the behaviour of closure operators under the lifting along the forgetful functor T from quasi-uniform spaces to topological spaces. By means of appropriate closure operators we compute the epimorphisms of many categories of quasi-uniform spaces defined by means of separation axioms and study the preservation (reflection) of epimorphisms under the functor T.     

On C‐Suslin spaces

We prove a closed graph theorem for Baire locally convex spaces (for Baire linear topological spaces) in the domain and weakly C‐Suslin locally convex spaces (respectively, for C‐Suslin linear topological spaces) in the range which improves some classic closed graph theorems and other, more recent, related results.     

On the measure of noncompactness of linear operators in spaces of strongly α-summable and bounded sequences

In this paper, we characterize classes of matrix transformations from BK spaces into spaces of bounded sequences and their subclasses of infinite matrices that define compact operators. Furthermore, using these results and the solvability of certain infinite linear systems we give necessary and sufficient conditions for A to be a compact operator on spaces that are strongly α-bounded or summable. Research is supported by the German DAAD foundation (German Academic Exchange Service), the University of Le Havre and the research project #1232 of the Serbian Ministry of Science, Technology and Development.     

Linear operators in finite dimensional probabilistic normed spaces

In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete.     

Interpolation of Herz Spaces and Applications

C. Herz introduced in [Hr] some new spaces to study properties of functions. An Interesting account, with many applications, of some particular cases of the generalized Herz spaces is given in [BS]. In this paper we first identify the duals of the generalized Herz spaces. Then, we characterize their intermediate spaces when the complex method of interpolation for families of spaces Is used. Applications are given that show the bounded ness of many operators on the generalized Herz spaces.     

Paranorm <Emphasis Type="Italic">I</Emphasis>-convergent sequence spaces

In this article we introduced the sequence spaces c ^I (p), c ₀ ^I (p), m ^I (p) and m ₀ ^I (p) for p = (p _k ), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition theorem and obtain some inclusion relations.      

Complemented copies of c0 in spaces of operators

We study the existence of complemented copies of c ₀ in certain Banach spaces of bounded linear operators and apply our results to spaces of bounded vector valued measures. This revised version was published online in June 2006 with corrections to the Cover Date.     

一类不可分解Banach空间上线性算子的谱性质

给出一类不可分解的∑_e~1型Banach空间上线性算子(不一定有界)的谱结构,并讨论这种空间上生成C_0群或C_0半群的线性算子的有界性、特殊的谱性质和谱结构,还给出这种空间上闭算子是有界算子的一个充分条件。