Some notes on complex symmetric operators
نویسندگان
چکیده
Abstract In this paper we show that every conjugation C on the Hardy-Hilbert space H 2 is of type = T *
منابع مشابه
Some Notes on Managing Closure Operators
It is widely known that closure operators on finite sets can be represented by sets of implications (also known as inclusion dependencies) as well as by formal contexts. In this paper we survey known results and present new findings concerning time and space requirements of diverse tasks for managing closure operators, given in contextual, implicational, or black-box representation. These tasks...
متن کاملComplex Symmetric Operators and Applications
We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, selfadjoint extensions of s...
متن کاملNotes on Some Fractional Calculus Operators and Their Properties
Here we state the main properties of the Caputo, Riemann-Liouville and the Caputo via Riemann-Liouville fractional derivatives and give some general notes on these properties. Some properties given in some recent literatures and used to solve fractional nonlinear partial differential equations will be proved that they are incorrect by giving some counter examples.
متن کاملComplex Symmetric Operators and Applications Ii
A bounded linear operator T on a complex Hilbert space H is called complex symmetric if T = CT ∗C, where C is a conjugation (an isometric, antilinear involution of H). We prove that T = CJ |T |, where J is an auxiliary conjugation commuting with |T | = √ T ∗T . We consider numerous examples, including the Poincaré-Neumann singular integral (bounded) operator and the Jordan model operator (compr...
متن کاملNotes on Creation Operators
Example 1 Let Bm = multiplication by the Schur function sm. The family {Bm} creates the homogeneous basis. Bm(sλ) is given by the Pieri rule. This implies that the homogeneous basis when expanded in terms of the Schur functions is given by bλ = ∑ μKμλsμ where the coefficients Kμλ are the column strict tableaux of shape μ and content λ. We could hope that a similar attack might work on more comp...
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: E-Journal of Analysis and Applied Mathematics
سال: 2021
ISSN: ['2544-9990']
DOI: https://doi.org/10.2478/ejaam-2021-0006