It has been proved recently [1] that a contraction, satisfying some complementary assumptions, is similar to a normal operator if and only if its resolvent grows at most linearly towards the spectrum.

Linear operators form the cornerstone of analysis in Banach spaces, offering a framework in which one can rigorously study continuity, spectral properties and stability. Banach space theory, with its ...

Let M be a von Neumann algebra and let φ be a normal linear functional on a strongly closed C*-subalgebra N of M. Denote by Fφ the set of normal linear functionals ψ on M extending φ with |ψ| = |φ|.

Linear operators form the backbone of modern mathematical analysis and have become indispensable in characterising the behaviour of dynamical systems. At their core, these operators are functions that ...