Non-commutative Clarkson Inequalities for n-Tuples of Operators

Hirzallah, Omar; Kittaneh, Fuad

doi:10.1007/s00020-008-1565-x

Cited by 29 publications

(15 citation statements)

References 15 publications

(17 reference statements)

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“…which is called the parallelogram law. Bhatia et al have obtained some generalizations of (2) to n-tuples of operators and many different conclusions by using various methods such as complex interpolation method and concavity and convexity of certain functions (see [3][4][5][6][7][8]).…”

Section: Introductionmentioning

confidence: 99%

Versions of Inequalities Related to p-Schatten Norm

Gao

Liu

Tian

2020

Journal of Function Spaces

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In this paper, we investigate some operator inequalities for the p-Schatten norm and obtain some other versions of these inequalities when parameters taking values in different regions. Let A1,…,An, B1,…,Bn∈BpH such that ∑i,j=1nAi∗Bj=0. Then, for p≥2, p≥λ>0, and 0<μ≤2, n21/p−1/λ∑i,j=1nAi±Bjpλ1/λ≤n1/2∑i=1nAi2+∑i=1nBi2p/21/2≤21/2−μ/4n1−μ/4∑i=1nAip4/μ+∑i=1nBip4/μμ/4. For 0<p≤2, p≤λ, and μ≥2, the inequalities are reversed. Moreover, we get some applications of our results.

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Section: Introductionmentioning

confidence: 99%

Versions of Inequalities Related to p-Schatten Norm

Gao

Liu

Tian

2020

Journal of Function Spaces

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“…There are several extensions of parallelogram law among them we could refer the interested reader to [4,5,11,16,17]. Generalizations of the parallelogram law for the Schatten pnorms have been given in the form of the celebrated Clarkson inequalities (see [9] and references therein). Since C 2 is a Hilbert space under the inner product A, B = tr(B * A),…”

Section: Introductionmentioning

confidence: 99%

An operator extension of the parallelogram law and related norm inequalities

Moslehian¹

2011

Mathematical Inequalities &Amp; Applications

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Abstract. We establish a general operator parallelogram law concerning a characterization of inner product spaces, get an operator extension of Bohr's inequality and present several norm inequalities. More precisely, let A be a C * -algebra, T be a locally compact Hausdorff space equipped with a Radon measure μ and let (A t ) t∈T be a continuous field of operators in A such that the function t → A t is norm continuous on T and the function t → A t is integrable. If α : T × T → C is a measurable function such that α(t,s)α(s,t) = 1 for all t,s ∈ T , then we show thatMathematics subject classification (2010): Primary 47A63; Secondary 46C15, 47A30, 47B10, 47B15, 15A60.

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“…There are several extensions of parallelogram law among them we could refer the interested reader to [2,3,6,9,10]. Generalizations of the parallelogram law for the Schatten p-norms have been given in the form of the celebrated Clarkson inequalities (see [4] and references therein). Since C 2 is a Hilbert space under the inner product A, B = tr(B * A), it follows from an equality similar to (1.2) stated for vectors of a Hilbert space (see [7,Corollary 2.7]) that if A 1 , .…”

Section: Introductionmentioning

confidence: 99%