Unilateral shift

1974 ◽  
pp. 268-285
Author(s):  
P. R. Halmos
Keyword(s):  
Unilateral Shift

On Quasisimilarity for Subnormal Operators, II

1982 ◽  
Vol 25 (1) ◽  
pp. 37-40 ◽  
Author(s):  
John B. Conway
Keyword(s):  
Subnormal Operator ◽  
Unilateral Shift ◽  
Closed Algebra ◽  
Subnormal Operators ◽  
Weak Star

AbstractLet S be a subnormal operator and let be the weak-star closed algebra generated by S and 1. An example of an irreducible cyclic subnormal operator S is found such that there is a T in with S and T quasisimilar but not unitarily equivalent. However, if S is the unilateral shift, T ∈ and S and T are quasisimilar, then S ≅ T.

scholarly journals Conjugations in $$L^2$$ and their invariants

2020 ◽  
Vol 10 (2) ◽  
Author(s):  
M. Cristina Câmara ◽  
Kamila Kliś–Garlicka ◽  
Bartosz Łanucha ◽  
Marek Ptak
Keyword(s):  
Hardy Space ◽  
Unit Circle ◽  
Unilateral Shift ◽  
Model Spaces

Abstract Conjugations in space $$L^2$$ L 2 of the unit circle commuting with multiplication by z or intertwining multiplications by z and $${{\bar{z}}}$$ z ¯ are characterized. We also study their behaviour with respect to the Hardy space, subspaces invariant for the unilateral shift and model spaces.

Involutory *-antiautomorphisms in Toeplitz algebras

1988 ◽  
Vol 103 (3) ◽  
pp. 473-480
Author(s):  
P. J. Stacey
Keyword(s):  
Hilbert Space ◽  
Orthonormal Basis ◽  
Compact Operators ◽  
Complex Hilbert Space ◽  
Unilateral Shift ◽  
Integral Power

Let H be a separable complex Hilbert space with orthonormal basis {ei: i ∈ ℕ}, let s be the unilateral shift defined by sei = ei+1 for each i and let K be the algebra of compact operators on H. The present paper classifies the involutory *-anti-automorphisms in the C*-algebra C*(sn, K) generated by K and a positive integral power sn of s. It is shown that, up to conjugacy by *-automorphisms, there are two such involutory *-antiautomorphisms when n is even and one when n is odd.

scholarly journals Efficient spectral regulation in Ce:Lu3(Al,Cr)5O12 and Ce:Lu3(Al,Cr)5O12/Ce:Y3Al5O12 transparent ceramics with high color rendering index for high-power white LEDs/LDs

2021 ◽  
Author(s):  
Tianyuan Zhou ◽  
Chen Hou ◽  
Le Zhang ◽  
Yuelong Ma ◽  
Jian Kang ◽  
...  
Keyword(s):  
Thermal Stability ◽  
High Power ◽  
White Led ◽  
Transparent Ceramics ◽  
Photoluminescence Excitation ◽  
Unilateral Shift ◽  
Excitation Mode ◽  
White Leds ◽  
Color Rendering Index ◽  
Color Rendering

AbstractRealizing a high color rendering index (CRI) in Ce:LuAG transparent ceramics (TCs) with desired thermal stability is essential to their applications in white LEDs/LDs as color converters. In this study, based on the scheme of configuring the red component by Cr3+ doping, an efficient spectral regulation was realized in Ce,Cr:LuAG TCs. A unilateral shift phenomenon could be observed in both photoluminescence (PL) and photoluminescence excitation (PLE) spectra of TCs. By constructing TC-based white LED/LD devices in a remote excitation mode, luminescence properties of Ce,Cr:LuAG TCs were systematically investigated. The CRI values of Ce:LuAG TC based white LEDs could be increased by a magnitude of 46.2%. Particularly, by combining the as fabricated Ce,Cr:LuAG TCs with a 0.5 at% Ce:YAG TC, surprising CRI values of 88 and 85.5 were obtained in TC based white LEDs and LDs, respectively. Therefore, Ce,Cr:LuAG TC is a highly promising color convertor for high-power white LEDs/LDs applied in general lighting and displaying.

scholarly journals The compression of a slant Hankel operator to H2

2003 ◽  
Vol 74 (88) ◽  
pp. 129-136
Author(s):  
Taddesse Zegeye ◽  
S.C. Arora
Keyword(s):  
Unit Circle ◽  
Complex Plane ◽  
Hankel Operator ◽  
Inner Product ◽  
Unilateral Shift

A slant Hankel operator K? with symbol ? in L?(T) (in short L?), where T is the unit circle on the complex plane, is an operator whose representing matrix M = (aij) is given by ai,j = (?,z-2i-j), where (?, ?) is the usual inner product in L2(T) (in short L2). The operator L? denotes the compression of K? to H2(T) (in short H2). We prove that an operator L on H2 is the compression of a slant Hankel operator to H2 if and only if U *L = LU2, where U is the unilateral shift. Moreover, we show that a hyponormal L? is necessarily normal and L? can not be an isometry.

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