Joseph G. Stampfli

Bio: Joseph G. Stampfli is an academic researcher. The author has contributed to research in topics: Dual norm & Schatten norm. The author has an hindex of 5, co-authored 5 publications receiving 342 citations.

One-dimensional perturbations of operators.

Abstract: 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

Quadratically hyponormal weighted shifts

Abstract: 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.

Derivations of nest algebras

Abstract: 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.