We prove a recursion formula for generating functions of certain renormalizations of ∗–moments of the DT(δ0, 1)–operator T , involving an operation ⊙ on formal power series and a transformation E that converts ⊙ to usual multiplication. This recursion formula is used to prove that all of these generating functions are rational functions, and to find a few of them explicitly. Introduction In com...

There is a subtle difference as far as the invariant subspace problem is concerned for operators acting on real Banach spaces and operators acting on complex Banach spaces. For instance, the classical hyperinvariant subspace theorem of V. I. Lomonosov [10] while true for complex Banach spaces is false for real Banach spaces. When one starts with a bounded operator on a real Banach space and the...

Suppose that {ek} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D be a diagonal operator with respect to the orthonormal basis {ek}. That is, D = ∑∞ k=1 λkek⊗ek, where {λk} is a bounded sequence of complex numbers. Let T = D + u1 ⊗ v1 + · · ·+ un ⊗ vn. Improving a result [2] of Foias et al., we show that if the vectors u1, . . . , un and v1, . . . , vn satis...

0 While the model theory for contraction operators (cf. [4]) is always a useful tool, it is particularly powerful when dealing with C 0 (1) operators. Recall that an operator T on a Hilbert space H is a C 0 (N)-operator (N = 1, 2. . .) if T ≤ 1, T n → 0 and, T n → 0 (strongly) when n → ∞ and rank(1 − T * T) = N. In particular, a C 0 (1) operator is unitarily equivalent to the compression of the...

Abstract. For each sequence {cn}n in l1(N) we define an operator A in the hyperfinite II1-factor R. We prove that these operators are quasinilpotent and they generate the whole hyperfinite II1-factor. We show that they have non-trivial, closed, invariant subspaces affiliated to the von Neumann algebra and we provide enough evidence to suggest that these operators are interesting for the hyperin...