Joint metrizability of subspaces and perfect mappings

Weight and metrizability of inverses under hereditarily irreducible mappings

The main purpose of this paper is to study the weight under hereditarily irreducible mappings between continua. The main result states that if f : X → Y is an hereditarily irreducible and surjective mapping of a D-continuum X, then w(X) = w(Y ).

Characteristic Functions and Joint Invariant Subspaces

Let T := [T1, . . . , Tn] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a “one-toone” correspondence between the joint invariant subspaces under T1, . . . , Tn, and the regular factorizations of the characteristic function ΘT associated with T . In particular, we prove that there is a non-trivial joint in...

Joint local quasinilpotence and common invariant subspaces

In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for N-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].

Mappings of the Sets of Invariant Subspaces of Null Systems

Let P and P ′ be (2k + 1)-dimensional Pappian projective spaces. Let also f : P → P∗ and f ′ : P ′ → P ′∗ be null systems. Denote by Gk(f) and Gk(f ′) the sets of all invariant k-dimensional subspaces of f and f ′, respectively. In the paper we show that if k ≥ 2 then any mapping of Gk(f) to Gk(f ′) sending base subsets to base subsets is induced by a strong embedding of P to P ′. MSC 2000: 51M...

Metrizability of Decomposition Spaces