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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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