Results 241 to 250 of about 3,589,565 (274)

On Variance and Covariance for Bounded Linear Operators

Acta Mathematica Sinica, English Series, 2001
Let \(H\) be a complex Hilbert space. For a vector \(0\neq y\in H\) and operators \(T,S\in B(H)\), \(\text{Cov}_{y}(S,T)\) and \(\text{Var}_{y}(S)\) are defined as \[ \begin{aligned} \text{Cov}_{y}(S,T)&= \|y\|^{2}(Sx,Tx)-(Sx,y)(y,Tx)\\ \text{and}\\ \text{Var}_{y}(S)&= \|y\|^{2}\|Sx\|^{2} -|(Sx,y)|^{2},\end{aligned} \] respectively.
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Bounded and Unbounded Linear Operators

2011
This chapter is devoted to the basic material on operator theory, semigroups, evolution familites, interpolation spaces, fractional powers of operators, intermediate spaces, and their basic properties needed in the sequel. Various illustrative examples are discussed in-depth. The estimates in Lemma 2.2 (Diagana et al. [52]) and Lemma 2.4 (Diagana [62])
Paul H. Bezandry, Toka Diagana
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Representation of Bounded Linear Operators

2013
In this final chapter we make a start on the difficult problem of representing linear maps (between Banach spaces) that are merely bounded. The magnitude of the task is underscored by the fact that even in a Hilbert space context, really satisfactory results are available only for normal operators. Moreover, the methods used in the spectral analysis of
David E. Edmunds, W. Desmond Evans
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Bounded and Unbounded Linear Operators

1987
Let H be a complex inner product space and let L(H) be the set of all bounded linear operators on H. In this chapter we present some basic facts about the set L(H) as well as about the set of unbounded operators on H. We also present some classes of operators whose structure is better understood, among which we mention the class of hermitian, unitary ...
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Euclidean Operator Radius Inequalities of a Pair of Bounded Linear Operators and Their Applications

Bulletin of the Brazilian Mathematical Society, 2022
Kallol Paul, Pintu Bhunia
exaly  

Bounded linear operators

2023
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A Modified Generalized Analytic Feynman Integral Associated with the Bounded Linear Operator

Axioms, 2022
Hyun Soo Chung
exaly  

q-Generalized Linear Operator on Bounded Functions of Complex Order

Mathematics, 2020
Rizwan Badar, Khalida Inayat Noor
exaly  

Bounded linear operators

2004
Yuli Eidelman, Vitali Milman, Antonis Tsolomitis   +2 more
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On the Norm Attainment Set of a Bounded Linear Operator and Semi-Inner-Products in Normed Spaces

Indian Journal of Pure and Applied Mathematics, 2020
Debmalya Sain
exaly