On regularity of compressions and diagonals of operator functions

2025/12/17 by Müller, Vladimir, Tomilov, Yuri
Mathematics · #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #Advanced Banach Space Theory

paper · doi:10.48550/arxiv.2512.15467

Abstract

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no analogues in the literature and rely on a new technique. The results are especially transparent for selfadjoint operators.

Citations

• Matrix representations of arbitrary bounded operators on Hilbert spaces
• Restricted invertibility of continuous matrix functions
• On interplay between operators, bases, and matrices
• Diagonals of operators and Blaschke's enigma
• Measurable selector in Kadison's carpenter's theorem
• Circles in the spectrum and the geometry of orbits: a numerical ranges approach
• Pinchings and Positive linear maps
• The Schur-Horn theorem for operators with finite spectrum
• An infinite dimensional Schur-Horn theorem and majorization theory with applications to operator ideals
• Compressions and Pinchings
• The inverse spectral problem for self-adjoint Hankel operators

Related

• The sandwich rule for sequences of self-adjoint operators and some applications
• Recent results on truncated Toeplitz operators
• Density Invariance of Certain Operational Quantities of Bounded Linear Operators in Normed Spaces
• Compressed resolvents of selfadjoint contractive extensions with exit and holomorphic operator-functions associated with them
• Total Dilations