Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication to vector model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that product $A_\Phi A_\Psi$ itself operator.

A linear operator on a Hilbert space may be approximated with nite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L2 functions are never compact; for them we consider how well the eigenvalues of the matrices approximate th...

This paper describes a Generalized Minimum Variance Control (GMVC) strategy for time varying systems (TVS). If GMVC applies to TVS, be conscious of the time varying multiplication, such as multiplying that comprises of more than two polynomials. In TVS, the time varying multiplication includes the time shift operator. The calculation of time shift multiplication was proposed by Zhen. Li. Howeve...

A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz ope...

We compute the norm of the restriction of a Schur multiplier, arising from a multiplication operator, to a coordinate subspace. This result is used to generalize Wielandt’s minimax inequality. Furthermore, we compute various s-numbers of an elementary Schur multiplier and determine criteria for membership of such multipliers in certain operator ideals.

We prove that the quadratic second quantization of an operator p on L2(Rd)∩L∞(Rd) is an orthogonal projection on the quadratic Fock space if and only if p = MχI , where MχI is a multiplication operator by a characteristic function χI .

Let S be the multiplication operator by an independent variable x in L2(0, 1) and V be an integral operator of Volterra type. We find conditions for T := S + V to be similar to S and discuss some generalisations of the results obtained to an abstract setting.

We show that b ∈ BMO( n) if and only if the commutator [b, Iα] of the multiplication operator by b and the fractional integral operator Iα is bounded from generalized Morrey spaces Lp,φ( n) to Lq,φ q/p ( n), where φ is non-decreasing, and 1 < p < ∞, 0 < α < n and 1/q = 1/p− α/n.