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 ...

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 ...

In this paper we show that binormal operators have nearest normal approximants. In fact, we exhibit nearest normals to such operators and, as a corollary, show that the hermitian part of a binormal ...