Numerical Analysis

Gustafson, Karl; Rao, Duggirala K. M.

doi:10.1007/978-1-4613-8498-4_4

Cited by 3 publications

(5 citation statements)

References 19 publications

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“…Since T is A-normal then by Theorem 2.16 (i), T is normal in R(A 1/2 ). Now, by applying [23, for the normal operator T , we obtain W ( T ) ⊆ conv(σ( T )). This relation together with Lemma 2.2 (iv) and Theorem 2.13 implies that…”

Section: Therefore We Obtainmentioning

confidence: 99%

Assessment of Modern Methods for Remote Teaching in Some Selected Educational Institutions in Kolkata City of West Bengal, India

Sen¹,

Goswami²

2023

Redefining Virtual Teaching Learning Pedagogy

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In this paper we explore the relation between the A-numerical range and the A-spectrum of A-bounded operators in the setting of semi-Hilbertian structure. We introduce a new definition of A-normal operator and prove that closure of the A-numerical range of an A-normal operator is the convex hull of the A-spectrum. We further prove Anderson's theorem for the sum of A-normal and A-compact operators which improves and generalizes the existing result on Anderson's theorem for A-compact operators. Finally we introduce strongly A-numerically closed class of operators and along with other results prove that the class of A-normal operators is strongly A-numerically closed.

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Section: Therefore We Obtainmentioning

confidence: 99%

Assessment of Modern Methods for Remote Teaching in Some Selected Educational Institutions in Kolkata City of West Bengal, India

Sen¹,

Goswami²

2023

Redefining Virtual Teaching Learning Pedagogy

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“…In particular, if T is normal (i.e. T * T = T T * ), then W (T ) = conv σ(T ) (see [7,). In addition, W (T ) ⊆ R if and only if T is self-adjoint (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, W (T ) ⊆ R if and only if T is self-adjoint (i.e. T * = T ) (see [7,). Moreover, it is well known that the numerical range of a direct sum is the convex hull of the numerical ranges of the summands.…”

Section: Introductionmentioning

confidence: 99%

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Operators with closed numerical ranges in nest algebras

Liang

2018

Proc. Amer. Math. Soc.

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In the present paper, we continue our research on numerical ranges of operators. With newly developed techniques, we show thatLet N be a nest on a Hilbert space H and T ∈ T (N ), where T (N ) denotes the nest algebra associated with N . Then for given ε > 0, there exists a compact operator K with K < ε such that T + K ∈ T (N ) and the numerical range of T + K is closed.As applications, we show that the statement of the above type holds for the class of Cowen-Douglas operators, the class of nilpotent operators and the class of quasinilpotent operators.

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“…. , A k ) is the set of simultaneously allowed expectation values taken over all mixed states [33][34][35], (4) where M d denotes the set of density operators of size d.…”

mentioning

confidence: 99%

Universal witnesses of vanishing energy gap

Szymański

Zyczkowski

2021

EPL

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Energy gap, the difference between the energy of the ground-state of a given Hamiltonian and the energy of its first excited state, is a parameter of a critical importance in analysis of phase transitions and adiabatic quantum computation. We present a concrete technique to determine an upper bound for the energy gap of a Hamiltonian H 0 based on properties of the set of expectation values of H 0 and an additional auxiliary Hamiltonian V. This formalism can be applied to obtain an effective criterion of gaplessness, which we illustrate with a concrete example of the XY model —a physical system with vanishing energy gap.

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Numerical Analysis

Cited by 3 publications

References 19 publications

Assessment of Modern Methods for Remote Teaching in Some Selected Educational Institutions in Kolkata City of West Bengal, India

Assessment of Modern Methods for Remote Teaching in Some Selected Educational Institutions in Kolkata City of West Bengal, India

Operators with closed numerical ranges in nest algebras

Universal witnesses of vanishing energy gap

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