Proper subspaces and compatibility

Proper Contractions and Invariant Subspaces

Let T be a contraction and A the strong limit of {T∗nTn}n≥1. We prove the following theorem: if a hyponormal contraction T does not have a nontrivial invariant subspace, then T is either a proper contraction of class 00 or a nonstrict proper contraction of class 10 for which A is a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator [T∗,T ] is a strict contracti...

Vector Spaces as Unions of Proper Subspaces

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces. 1. The main theorem Consider the following well-known problem in linear algebra (which is used, for example, to produce vecto...

Hyperinvariant subspaces and quasinilpotent operators

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

ε-weakly Chebyshev subspaces and quotient spaces

The function of scs , Rf , and vi for proper compatibility of durum wheat nucleus in alien

Our project is to measure differential responses of various alien cytoplasms in a specific nuclear background to various pathogens to provide a better understanding on the effect of nuclear-cytoplasmic interactions on biotic stress tolerance. In this study, we analyzed the nuclear donors of 56-1 (tetraploid), and Chris and Selkirk (both hexaploid), alloplasmic lines. Fifty selected alloplasmic ...