Bohr phenomenon for operator-valued functions
نویسندگان
چکیده
Abstract We establish Bohr inequalities for operator-valued functions, which can be viewed as analogues of a couple interesting results from scalar-valued settings. Some this paper are motivated by the classical flavour inequality, while others based on generalized concept radius problem.
منابع مشابه
Denseness for norm attaining operator-valued functions
In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss’ famous result on the denseness of norm attaining operators. Specifically, we show given any A ∈ L(H) there is a sequence of rank-1 operators Kn such that A+Kn is norm attaining for each n and Kn converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operato...
متن کاملRemarks on the Bohr Phenomenon
Bohr’s theorem ([10]) states that analytic functions bounded by 1 in the unit disk have power series ∑ anz n such that ∑ |an||z| < 1 in the disk of radius 1/3 (the so-called Bohr radius.) On the other hand, it is known that there is no such Bohr phenomenon in Hardy spaces with the usual norm, although it is possible to build equivalent norms for which a Bohr phenomenon does occur! In this paper...
متن کاملR-boundedness of Smooth Operator-valued Functions
In this paper we study R-boundedness of operator families T ⊂ B(X, Y ), where X and Y are Banach spaces. Under cotype and type assumptions on X and Y we give sufficient conditions for R-boundedness. In the first part we show that certain integral operator are R-bounded. This will be used to obtain R-boundedness in the case that T is the range of an operator-valued function T : Rd → B(X, Y ) whi...
متن کاملFinite rank harmonic operator-valued functions
The purpose of this paper is to characterize when a harmonic function with values in the finite rank operators on a Hilbert space is expressible as a harmonic matrix-valued function. We show that harmonic function with values in the rank 1 normal operators is expressible as a harmonic matrix-valued function. We also prove that for any natural number, n, a harmonic function with values in the ra...
متن کاملSome Applications of Operator-valued Herglotz Functions
We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model operators for both situations, linear fractional transformations for Herglotz operators, results on Friedrichs and Krein extensions, and realization theorems for cla...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2021
ISSN: ['1464-3839', '0013-0915']
DOI: https://doi.org/10.1017/s0013091520000395