Complex Symmetric Operators and Applications II

By Stephan Ramon Garcia, Mihai Putinar. 2005

385 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c0212206f558e569ce0224593b0ed00cb2b240cf

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Citations in the corpus

Aluthge Transforms of Complex Symmetric Operators (2008, neutral): “We refer the reader to [18, 19] (or [20] for a more expository pace) for further details.”
THE CHARACTERISTIC FUNCTION OF A COMPLEX SYMMETRIC CONTRACTION (2006, methodology): “We first recall some basic facts from [3, 4, 5 ]. Let H be a complex Hilbert space, and L(H) the algebra of all bounded linear operators on H. A conjugation C on H is an anti-linear, isometric and involutive map; thus C2 = I, and hCf,Cgi = hg,fi for all f,g 2 H. It is easy to see that”
Conjugation and Clark Operators (2006, background): “example, we discuss an explicit parameterization of the noncyclic functions for the backward shift operator and show that compressed shifts and their associated Clark operators [10] belong to the class of complex symmetric operators [ 23 , 24].”
On local spectral properties of complex symmetric operators (2011, background): “This class includes all normal operators, Hankel operators, compressed Toeplitz operators, and the Volterra integration operator, and there are a lot of consequences and applications concerning complex symmetric operators (see [10–16,26], etc.”
Real Linear Operator Theory and its Applications (2011, background): “1 We do not insist on κ being an isometry which is occasionally required [ 9 ].”
Recent Progress on Truncated Toeplitz Operators (2011, background): “ion now toward unitary equivalence. Let us begin by recalling an early result of Sarason, who observed that the Volterra integration operator (1.1), a standard example of a complex symmetric operator [45,53,54], is unitarily equivalent to a truncated Toeplitz operator acting on the Ku space correspo”
Algebras of truncated Toeplitz operators (2010, background): “ontains Dand so these boundary reproducing kernels are deﬁned for every unimodular ζ. Truncated Toeplitz operators have a symmetry property called Csymmetry. This concept is due to Garcia and Putinar [6, 7, 8]. Given a C-Hilbert space H and an antilinear isometric involution C on H, we say that a bo”
Which Weighted Composition Operators are Complex Symmetric (2011, neutral): “Wogen, in various combinations, in [7–10].”
Complex symmetric weighted composition operators on H2(D) (2014, background): “We refer the reader to [13,15–18], and [26] for more details, including historical comments and references.”
Some new classes of complex symmetric operators (2009, methodology): “Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data (dim ker T,dim ker T ∗).”
Truncated Toeplitz Operators on Finite Dimensional Spaces (2008, background): “Garcia and Putinar in [ 4 ] show thatfe 1; ;e ng is an orthonormal basis which not only diagonalizes the Clark operator U but has the additional property that the matrix representation of any truncated Toeplitz operator with respect to this basis is complex symmetric.”
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, and Similarity (2009, background): “one can show that dimTΘ = 2n−1 (see Lemma 2.17 below). Complex symmetric operators. Of particular importance to the study of truncated Toeplitz operators is the notion of a complex symmetric operator [11, 12]. Let us brieﬂy discuss the necessary preliminaries. In the following, we let H denote a sep”