Norm estimates of ω-circulant operator matrices and isomorphic operators for ω-circulant algebra

Jiang, Zhaolin; Xu, Tao

doi:10.1007/s11425-015-5051-z

Cited by 11 publications

(3 citation statements)

References 37 publications

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“…where RSFPLRcircfc(T CUML ) is the row skew first-plus-last right circulant with the same first column as that of T CUML , and L(a i ) is the lower triangular Toeplitz matrix with the first column a i = (a i0 , a i1 , · · · , a i,n−1 ) T , and SCirc(b T i ) is the skew circulant matrix with the first row [17,19,22,33]. Theorem 3.2.…”

Section: Theorem 31 If the Equalitymentioning

confidence: 99%

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Jiang¹,

Hong²,

Fu³

2017

J. Nonlinear Sci. Appl.

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In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are " similar" to the Toeplitz matrices. Their (−1, −1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (−1, 1)-circulants and (1, −1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.

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Section: Theorem 31 If the Equalitymentioning

confidence: 99%

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Jiang¹,

Hong²,

Fu³

2017

J. Nonlinear Sci. Appl.

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“…Works on norm equalities and inequalities of special kind of operator matrices can be found in the literature [ 2 , 7 , 25 , 26 ]. Jiang and Xu [ 23 ] explored special cases for norm equalities and inequalities, such as usual operator norm and Schatten p-norms. Several norm equalities and inequalities for the circulant, skew circulant, and w-circulant operator matrices were studied [ 4 , 23 ].…”

Section: Introductionmentioning

confidence: 99%

“…Jiang and Xu [ 23 ] explored special cases for norm equalities and inequalities, such as usual operator norm and Schatten p-norms. Several norm equalities and inequalities for the circulant, skew circulant, and w-circulant operator matrices were studied [ 4 , 23 ].…”

Section: Introductionmentioning

confidence: 99%

On $${\mathbb {A}}$$-numerical radius equalities and inequalities for certain operator matrices

Kittaneh

Sahoo

2021

Ann. Funct. Anal.

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The main goal of this article is to establish several new -numerical radius equalities for n × n circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where is the n × n diagonal operator matrix whose diagonal entries are positive bounded operator A. Some special cases of our results lead to the results of earlier works in the literature, which shows that our results are more general. Further, some pinching type -numerical radius inequalities for n × n block operator matrices are given. Some equality conditions are also given. We also provide a concluding section, which may lead to several new problems in this area.

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Norm equalities and inequalities for three circulant operator matrices

Jiang

Qiao

Wang

2016

Acta. Math. Sin.-English Ser.

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Norm estimates of ω-circulant operator matrices and isomorphic operators for ω-circulant algebra

Cited by 11 publications

References 37 publications

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

On $${\mathbb {A}}$$-numerical radius equalities and inequalities for certain operator matrices

Norm equalities and inequalities for three circulant operator matrices

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