Numerical radius inequalities for tensor product of operators

Bhunia, Pintu; Paul, Kallol; Sen, Anirban

doi:10.1007/s12044-022-00722-2

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…It has been shown in [8] that For other inequalities concerning tensorial product, see [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Tensorial and Hadamard Product Inequalities for Synchronous Functions

DRAGOMIR

2023

Communications in Advanced Mathematical Sciences

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Let H be a Hilbert space. In this paper we show among others that, if f, g are synchronous and continuous on I and A, B are selfadjoint with spectra Sp(A), Sp(B)⊂I, then (f(A)g(A))⊗1+1⊗(f(B)g(B))≥f(A)⊗g(B)+g(A)⊗f(B) and the inequality for Hadamard product (f(A)g(A)+f(B)g(B))∘1≥f(A)∘g(B)+f(B)∘g(A). Let either p,q∈(0,∞) or p,q∈(-∞,0). If A, B>0, then A^{p+q}⊗1+1⊗B^{p+q}≥A^{p}⊗B^{q}+A^{q}⊗B^{p}, and (A^{p+q}+B^{p+q})∘1≥A^{p}∘B^{q}+A^{q}∘B^{p}.

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“…It has been shown in [8] that For other inequalities concerning tensorial product, see [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Tensorial and Hadamard Product Inequalities for Synchronous Functions

DRAGOMIR

2023

Communications in Advanced Mathematical Sciences

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“…For further readings on the numerical radius, we refer to [7,16]. It is well known that ( [10, p. 44] and [4]) if A = [a ij ] is an n × n complex matrix such that a ij ≥ 0 for all i, j = 1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

Numerical Radius of Operator Matrices and Applications

Bhunia

Dragomir

Moslehian

et al. 2022

Infosys Science Foundation Series

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Let A = [A ij ] be an n × n operator matrix where each A ij is a bounded linear operator on a complex Hilbert space H. With other numerical radius bounds via contraction operators, we show that w(A) ≤ w( Ã), where Ã = [a ij ] is an n × n complex matrix withThis bound refines the well known bound w(A) ≤ w( Â), where Â Appl. 468 (2015), 18-26]. We deduce that if A, B are bounded linear operators on H, thenFurther by applying the numerical radius bounds of operator matrices, we deduce some numerical radius bounds for a single operator, the product of two operators, the commutator of operators. We show that if A is a bounded linear operator on H, then w(A) ≤ 1 2 A t |A| 1−t + |A * | 1−t for all t ∈ [0, 1], which refines as well as generalizes the existing ones.

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Sharper bounds for the numerical radius of $${n}\times {n}$$ operator matrices

Bhunia

2024

Arch. Math.

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Numerical radius inequalities for tensor product of operators

Cited by 4 publications

References 15 publications

Tensorial and Hadamard Product Inequalities for Synchronous Functions

Tensorial and Hadamard Product Inequalities for Synchronous Functions

Numerical Radius of Operator Matrices and Applications

Sharper bounds for the numerical radius of $${n}\times {n}$$ operator matrices

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