/pdf/ten-problems-in-hilbert-space-3lzrzwfkny.pdf

Ten problems in Hilbert space

Orthogonality of matrices and some distance problems

O/ 00 Let T be a unilateral weighted shift with weight sequence { n}n= 0. We obtain a characterization of k-hyponormality for T in terms of the a n' s, and use it to show that if T is 2-hyponormal (i.e., (T, T 2) jointly hyponormal) and c~ n = an+ 1 for some n, then T must be subnormal, i.e., al = a2 .... . If T is only quadratically hyponormal (i.e., T + AT 2 is hyponormal for all A E f), and a n = an+ 1 = an+2, T must also be subnormal; however, two equal weights do not necessarily force subnormality. As a matter of fact, if T x is the shift with weights o~ 0 = x, al = ~-/-3' a2 = ~-~' a3 = (4~-5' etc., we show that T x is quadratically hyponormal if and only if x < (~-3, and that T x is 2-hyponormal if and only if x < 3/4. Also, for a given k, T x gives rise to weighted shifts which are k-hyponormal but not (k+l)-hyponormal.

Quadratically hyponormal weighted shifts

Recursively generated weighted shifts and the subnormal completion problem, II

The results presented below are generalisations of some well known results about yon Neumann algebras. The first result, Theorem 2.1, yields a sufficient condition for automatic continuity of any derivation of an algebra of operators into a dual normal module. The theorem is followed by a corollary which shows that reflexive algebras with commutative subspace lattices have only continuous derivations into dual normal modules. The second result, Theorem 3.6, is quite independent of the former. In Section 3 we prove that, for any nest algebra ~¢ and any ultraweakly closed algebra ~ of operators, the first cohomology group Hl (d ,9~) always vanishes. We ought perhaps to mention, that nest algebras are reflexive and do have commutative lattices of invariant subspaces.

/pdf/derivations-of-nest-algebras-3etbjek8n5.pdf

Derivations of nest algebras

/pdf/the-norm-of-a-derivation-uvwxkbd2h7.pdf

The norm of a derivation

/pdf/which-weighted-shifts-are-subnormal-2kntt7nznw.pdf

Which weighted shifts are subnormal

/pdf/minimal-range-theorems-for-operators-with-thin-spectra-1wtwdqog6a.pdf

Minimal range theorems for operators with thin spectra.

On montre que certains operateurs de rang un de norme petite comporte un morceau unitaire a partir du decalage. On exhibe un operateur normal dont la structure d'espace propre est alteree par l'addition d'un operateur de rang 1

/pdf/one-dimensional-perturbations-of-operators-43asb50s0b.pdf

One-dimensional perturbations of operators.

/pdf/on-selfadjoint-derivation-ranges-c3xlmsnzx5.pdf

Joseph G. Stampfli

Papers

The norm of a derivation

Which weighted shifts are subnormal

Minimal range theorems for operators with thin spectra.

One-dimensional perturbations of operators.

On selfadjoint derivation ranges.