Hyponormal and strongly hyponormal matrices in inner product spaces

Quasihyponormal and strongly hyponormal matrices in inner product spaces

Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products

It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An e...

Ela Quasihyponormal and Strongly Quasihyponormal Matrices in Inner Product Spaces

where 〈·, ·〉 denotes the standard inner product on C. If the Hermitian matrix H is invertible, then the indefinite inner product is nondegenerate. In that case, for every matrix T ∈ C, there is the unique matrix T [∗] satisfying [T x, y] = [x, T y] for all x, y ∈ C, and it is given by T [∗] = HT H . In these spaces, the notion of H-quasihyponormal matrix can be introduced by analogy with the qu...

Quartically Hyponormal Weighted Shifts Need Not Be 3-hyponormal

We give the first example of a quartically hyponormal unilateral weighted shift which is not 3-hyponormal.

Ela Hyponormal Matrices and Semidefinite Invariant Subspaces in Indefinite Inner Products

It is shown that, for any given polynomially normal matrix with respect to an indefinite inner product, a nonnegative (with respect to the indefinite inner product) invariant subspace always admits an extension to an invariant maximal nonnegative subspace. Such an extension property is known to hold true for general normal matrices if the nonnegative invariant subspace is actually neutral. An e...