Which weighted shifts are subnormal

One-step extensions of subnormal 2-variable weighted shifts

Which subnormal Toeplitz operators are either normal or analytic ?

We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos’s Problem 5: Which subnormal block Toeplitz operators are either normal or analytic ? We extend and prove Abrahamse’s Theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol ...

Finite Groups Whose «-maximal Subgroups Are Subnormal

Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...

Observing Children Who Are Severely Subnormal

as possible. The author shows the importance of communication with the severely subnormal child and of correct timing and imagination in the teacher's responses to him. She points out the value, on occasions, of observing the child without being involved and suggests useful ways of achieving this. Her points are well illustrated by case histories and actual observations made by students in the ...

On Polynomially Bounded Weighted Shifts

(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...