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.

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Let X be a hypergroup. In this paper, we study the homomorphisms on certain subspaces of L(X)* which are weak*-weak* continuous.

The different methods of reducing decoherence in quantum devices are discussed from the unified point of view based on the energy conservation principle and the concept of forbidden transitions. Minimal decoherence model, " bang-bang " techniques, Zeno effect and decoherence-free subspaces and subsystems are studied as particular examples.

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.

Let V denote an r-dimensional vector space over F q n , the finite field of elements. Then is also r n-dimension . An -subspace U ( h k ) -evasive if it meets h-dimensional -subspaces in dimension at most k. The 1 subspaces are known as scattered and they have been intensively studied geometry, their maximum size has proved to be ? ? 2 ? when even or = 3. We investigate subspaces, study two dua...