Ranges of nonlinear asymptotically linear operators

Tracial Numerical Ranges and Linear Dependence of Operators

Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.

Ela Tracial Numerical Ranges and Linear Dependence of Operators

Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.

Numerical ranges of composition operators

Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 i...

Subspace-diskcyclic sequences of linear operators

A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

Matrix Ranges of Operators on Hileert