New extended Weyl type theorems
Non-analytic local spectral properties in several variables
Nonhermitian systems and pseudospectra
Four applications are outlined of pseudospectra of highly nonnormal linear operators.
Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials.
Norm continuity of -semigroups
We show that a positive semigroup on with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the -scale, which may be of independent interest.
Note on the spectral inclusion theorem for Toeplitz operators
Note to the paper by R. Hempel, A. M. Hinz, and H. Kalf: On the Essential Spectrum of Schrödinger Operators with Spherically Symmetric Potentials.
Notes on q-deformed operators
The paper concerns operators of deformed structure like q-normal and q-hyponormal operators with the deformation parameter q being a positive number different from 1. In particular, an example of a q-hyponormal operator with empty spectrum is given, and q-hyponormality is characterized in terms of some operator inequalities.
Notes on the Taylor joint spectrum of commuting operators
Numerical range preserving operators on a Banach algebra