On the local spectral properties of the left multiplication operators

2011 ◽

Vol 22 (02) ◽

pp. 201-222 ◽

Cited By ~ 11

Author(s):

XIAOLI KONG ◽

HONGJIA CHEN ◽

CHENGMING BAI

Keyword(s):

Virasoro Algebra ◽

Indecomposable Module ◽

Multiplication Operators ◽

Algebraic Structures ◽

Witt Algebra ◽

Left Multiplication ◽

Symmetric Algebras ◽

Nonlinear Math ◽

Math Phys

We find that a compatible graded left-symmetric algebraic structure on the Witt algebra induces an indecomposable module V of the Witt algebra with one-dimensional weight spaces by its left-multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebraic structures on the Witt algebra are classified. All of them are simple and they include the examples given by [Comm. Algebra32 (2004) 243–251; J. Nonlinear Math. Phys.6 (1999) 222–245]. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebraic structures on the Virasoro algebra. They coincide with the examples given by [J. Nonlinear Math. Phys.6 (1999) 222–245].

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Mixing property of $$C_0$$ C 0 -semigroup of left multiplication operators

Bollettino dell Unione Matematica Italiana ◽

10.1007/s40574-015-0042-0 ◽

2015 ◽

Vol 8 (4) ◽

pp. 257-263 ◽

Cited By ~ 1

Author(s):

Ali Reza Sazegar ◽

Amanollah Assadi ◽

Omid Rabieimotlagh

Keyword(s):

Multiplication Operators ◽

Left Multiplication ◽

Mixing Property

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Spectral Properties of Multiplication Operators on Invariant Subspaces of the Bergman Space

Complex Variables Theory and Application An International Journal ◽

10.1080/027810703100015310 ◽

2003 ◽

Vol 48 (8) ◽

pp. 649-655 ◽

Cited By ~ 2

Author(s):

Kehe Zhu

Keyword(s):

Bergman Space ◽

Spectral Properties ◽

Invariant Subspaces ◽

Multiplication Operators

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Pre-jordan Algebras

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-15231 ◽

2013 ◽

Vol 112 (1) ◽

pp. 19 ◽

Cited By ~ 9

Author(s):

Dongping Hou ◽

Xiang Ni ◽

Chengming Bai

Keyword(s):

Lie Algebras ◽

Jordan Algebra ◽

Symplectic Form ◽

Jordan Algebras ◽

Multiplication Operators ◽

Baxter Equation ◽

Algebraic Structures ◽

Left Multiplication ◽

Close Relationship ◽

Dendriform Algebras

The purpose of this paper is to introduce and study a notion of pre-Jordan algebra. Pre-Jordan algebras are regarded as the underlying algebraic structures of the Jordan algebras with a nondegenerate symplectic form. They are the algebraic structures behind the Jordan Yang-Baxter equation and Rota-Baxter operators in terms of $\mathcal{O}$-operators of Jordan algebras introduced in this paper. Pre-Jordan algebras are analogues for Jordan algebras of pre-Lie algebras and fit into a bigger framework with a close relationship with dendriform algebras. The anticommutator of a pre-Jordan algebra is a Jordan algebra and the left multiplication operators give a representation of the Jordan algebra, which is the beauty of such a structure. Furthermore, we introduce a notion of $\mathcal{O}$-operator of a pre-Jordan algebra which gives an analogue of the classical Yang-Baxter equation in a pre-Jordan algebra.

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Some algebraic properties of F(X) and K(X)

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500010452 ◽

1975 ◽

Vol 19 (4) ◽

pp. 353-361 ◽

Cited By ~ 1

Author(s):

Freda E. Alexander

Keyword(s):

Banach Space ◽

Finite Rank ◽

Approximation Property ◽

Reflexive Banach Space ◽

Compact Operators ◽

Multiplication Operators ◽

Weakly Compact ◽

Dual Algebra ◽

Left Multiplication ◽

Algebraic Properties

Throughout we consider operators on a reflexive Banach space X. We consider certain algebraic properties of F(X), K(X) and B(X) with the general aim of examining their dependence on the possession by X of the approximation property. B(X) (resp. K(X)) denotes the algebra of all bounded (resp. compact) operators on X and F(X) denotes the closure in B(X) of its finite rank operators. The two questions we consider are:(1) Is K(X) equal to the set of all operators in B(X) whose right and left multiplication operators on F(X) (or on B(X)) are weakly compact?(2) Is F(X) a dual algebra?

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Model of multicomponent narrow-band periodical non-stationary random signal

Information extraction and processing ◽

10.15407/vidbir2020.48.017 ◽

2020 ◽

Vol 2020 (48) ◽

pp. 17-24

Author(s):

I.M. Javorskyj ◽

◽

R.M. Yuzefovych ◽

P.R. Kurapov ◽

◽

...

Keyword(s):

Time Series ◽

Real Time ◽

Hilbert Transform ◽

Spectral Properties ◽

Narrow Band ◽

Analytic Signal ◽

Random Signal ◽

Hilbert Transformation ◽

The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

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