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Compact Operators. Equations with Compact Operators
1996In this chapter, we study an important class of linear continuous operators, namely, compact (or completely continuous) operators. On the one hand, compact operators are interesting because they inherit many properties of operators in finite-dimensional spaces.
Georgij F. Us +2 more
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On Reflexive Compact Operators
Canadian Journal of Mathematics, 1977Let A be a compact operator on a separable Hilbert space . The aim of this paper is to investigate the relationship between the weak closure of the algebra of polynomials in A (denoted by U(A)) and its invariant subspace lattice Lat A.
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On Compact Perturbations of Operators
Canadian Journal of Mathematics, 1974Recently R. G. Douglas showed [4] that if V is a nonunitary isometry and U is a unitary operator (both acting on a complex, separable, infinite dimensional Hilbert space ), then V — K is unitarily equivalent to V ⊕ U (acting on ⊕ ) where K is a compact operator of arbitrarily small norm.
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Integral Equations and Operator Theory, 1984
Let H be a separable Hilbert space, T a compact bounded linear operator in H, \(\phi =\{\phi_ j\}^{\infty}_{j=1}\) an orthonormal basis of H. Then \(\phi \in Dom\{tr T\}\) if the series \(\sum^{\infty}_{j=1}\) converges, and if so, the sum is denoted by \(tr_{\phi}T\).
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Let H be a separable Hilbert space, T a compact bounded linear operator in H, \(\phi =\{\phi_ j\}^{\infty}_{j=1}\) an orthonormal basis of H. Then \(\phi \in Dom\{tr T\}\) if the series \(\sum^{\infty}_{j=1}\) converges, and if so, the sum is denoted by \(tr_{\phi}T\).
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Israel Journal of Mathematics, 1971
We consider the following problem: Does there exist a separable Banach spaceZ such that every compact operator can be factored as a productTS withT, S compact, rangeS=DomainT=Z? Our investigation yields a reasonable partial solution to this problem as well as the following independent result: A Banach space which has theλ-metric approximation property ...
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We consider the following problem: Does there exist a separable Banach spaceZ such that every compact operator can be factored as a productTS withT, S compact, rangeS=DomainT=Z? Our investigation yields a reasonable partial solution to this problem as well as the following independent result: A Banach space which has theλ-metric approximation property ...
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1993
In a sense, nonlinear analysis doesn’t require a very long attention span. A few chapters ago, we were concerned with algebraic topology in the theory of the Brouwer degree; the previous chapter gave us a brief but bracing dip into the sea of point-set topology; and in this chapter we will discuss some topics in classical “linear” functional analysis.
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In a sense, nonlinear analysis doesn’t require a very long attention span. A few chapters ago, we were concerned with algebraic topology in the theory of the Brouwer degree; the previous chapter gave us a brief but bracing dip into the sea of point-set topology; and in this chapter we will discuss some topics in classical “linear” functional analysis.
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1989
In this chapter we briefly explain the basic properties of bounded linear operators and then introduce the concept of compact operators that is of fundamental importance in the study of integral equations.
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In this chapter we briefly explain the basic properties of bounded linear operators and then introduce the concept of compact operators that is of fundamental importance in the study of integral equations.
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OSQP: an operator splitting solver for quadratic programs
Mathematical Programming Computation, 2020Bartolomeo Stellato +2 more
exaly
A guide for maximizing the accuracy of intraoral digital scans. Part 1: Operator factors
Journal of Esthetic and Restorative Dentistry, 2023Marta Revilla-León
exaly