For a bounded linear operator 𝑇 on a complex Hilbert space and 𝑛 ∈ ℕ, 𝑇 is said to be 𝑛-normal if 𝑇*𝑇𝑛 = 𝑇𝑛𝑇*. In this paper we show that if 𝑇 is a 2-normal operator and satisfies σ(𝑇)⋂(-σ ...

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 ...

Journal of Operator Theory, Vol. 48, No. 1 (Summer 2002), pp. 151-186 (36 pages) Motivated by recent developments in the theory of quantum groups, some classes of q-deformed operators (q-normal, ...

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 ...

A linear depth quantum circuit that implements general duality transformations in one dimensional quantum lattice models. Credit: Physical Review Letters (2025). DOI: 10.1103/PhysRevLett.134.130403 In ...