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Absolutely Summing Terraced Matrices

Ibrahim Almasri (2016)

Concrete Operators

Let α > 0. By Cα we mean the terraced matrix defined by [...] if 1 ≤ k ≤ n and 0 if k > n. In this paper, we show that a necessary and sufficient condition for the induced operator on lp, to be p-summing, is α > 1; 1 ≤ p < ∞. When the more general terraced matrix B, defined by bnk = βn if 1 ≤ k ≤ n and 0 if k > n, is considered, the necessary and sufficient condition turns out to be [...] in the region 1/p + 1/q ≤ 1.

Factorization of unbounded operators on Köthe spaces

T. Terzioğlu, M. Yurdakul, V. Zahariuta (2004)

Studia Mathematica

The main result is that the existence of an unbounded continuous linear operator T between Köthe spaces λ(A) and λ(C) which factors through a third Köthe space λ(B) causes the existence of an unbounded continuous quasidiagonal operator from λ(A) into λ(C) factoring through λ(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (λ(A),λ(B)) ∈ ℬ (which means that all...

Factorization through Hilbert space and the dilation of L(X,Y)-valued measures

V. Mandrekar, P. Richard (1993)

Studia Mathematica

We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.

The support of the associated measure to the Cowen's tridiagonal matrix.

Dolores Barrios, Venancio Tomeo, Emilio Torrano (1994)

Extracta Mathematicae

In this paper we consider a class of three-term recurrence relations, whose associated tridiagonal matrices are subnormal operators. In this cases, there are measures associated to the polynomials given by such relations. We study the support of these measures.

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