We give descriptions of SSDand QP -points in C(K)-spaces and use this to characterize strongly proximinal subspaces of finite codimension in L1(μ). We provide some natural class of examples of strongly proximinal subspaces which are not necessarily finite codimensional. We also study transitivity of strong proximinal subspaces of finite codimension.

A multilinear approach based on Grassmann representatives and matrix compounds is presented for the identification of reducing pairs of subspaces that are common to two or more matrices. Similar methods are employed to characterize the deflating pairs of subspaces for a regular matrix pencil A+ sB, namely, pairs of subspaces (L,M) such that AL ⊆ M and BL ⊆ M.

Given two chains of subspaces in C, the set of those unitary matrices is studied that map the subspaces in the first chain onto the corresponding subspaces in the second chain, and minimize the value ‖U − In‖ for various unitarily invariant norms ‖ · ‖ on Cn×n. In particular, a formula for the minimum value ‖U − In‖ is given, and the set of all the unitary matrices in the set attaining the mini...

A closed subspace M in a Banach space X is called t/-proximinal if it satisfies: (1 + p)S n (S + M) ç S + e(pXS n M), for some positive valued function t(p), p > 0, and e(p) -» 0 as p -> 0, where 5 is the closed unit ball of X. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are (/-proximinal, for ...

For subspaces, X and Y , of the space, D, of all derivatives M(X, Y ) denotes the set of all g ∈ D such that fg ∈ Y for all f ∈ X. Subspaces of D are defined depending on a parameter p ∈ [0,∞]. In Section 6, M(X, D) is determined for each of these subspaces and in Section 7, M(X, Y ) is found for X and Y any of these subspaces. In Section 3, M(X, D) is determined for other spaces of functions o...

A method based on the algorithmization of the geometric approach, using the equivalence between the maximal unobservable subspaces and the maximal (A, B)-invariant subspaces is proposed in order to solve the problem of group decoupling for linear multivariable systems. Necessary and sufficient conditions for compatibility of the maximal controllability subspaces are transformed to the necessary...

In this paper we define k-elliptic sheaves, A-motives and t-modules over A, which are obvious generalizations of elliptic sheaves, t-motives and t-modules. Following results of [An1], [D], [LRSt], [Mu], [St],... we shall obtain the equivalence of this objects. Bearing in mind [Al] we also describe a correspondence between k-elliptic sheaves with formal level structures (2.9) and discrete subspa...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.