Anticoherent subspaces

“Anticoherent” Spin States via the Majorana Representation

In this article we define and exhibit “anticoherent” spin states, which are in a sense “the opposite” of the familiar coherent spin states. Since the familiar coherent states are as “classical” as spin states can be, the anticoherent states may turn out to be better candidates for applications involving non-classical behaviors such as quantum entanglement. Thanks to the Majorana representation ...

Covering of subspaces by subspaces

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and...

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.

Approximating weak Chebyshev subspaces by Chebyshev subspaces

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.

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