Abstract/Overview
Let X be a Banach space and T: X→Y be a linear operator, then Tis compact if it maps bounded sequences in X to sequences in Y with convergent subsequences, that is, if xn ∈ X is a bounded sequence, then T xn ∈ Y has a convergent subsequence say, T xnk in Y. The eigenvalue of an operator T, is a scalar λ if there is a nontrivial solution x such that T x=λ x. Such an x is called an eigenvector corresponding to the eigenvalue λ. A vector space is complete if every Cauchy sequence in V converges in V. It is known that every finite dimensional nor medspace is complete and that a Hilbert space is a normed space that is complete with respect to the norm induced by the inner product. In this paper we have established the conditions for completeness of a compact operator T whose norm is an eigenvalue.
N.</div>, < (2024). On Compact Operators Whose Norms Are Eigenvalues and Completeness. Afribary. Retrieved from https://afribary.com/works/on-compact-operators-whose-norms-are-eigenvalues-and-completeness
N.</div>, <div>Owino "On Compact Operators Whose Norms Are Eigenvalues and Completeness" Afribary. Afribary, 04 Jun. 2024, https://afribary.com/works/on-compact-operators-whose-norms-are-eigenvalues-and-completeness. Accessed 16 Sep. 2024.
N.</div>, <div>Owino . "On Compact Operators Whose Norms Are Eigenvalues and Completeness". Afribary, Afribary, 04 Jun. 2024. Web. 16 Sep. 2024. < https://afribary.com/works/on-compact-operators-whose-norms-are-eigenvalues-and-completeness >.
N.</div>, <div>Owino . "On Compact Operators Whose Norms Are Eigenvalues and Completeness" Afribary (2024). Accessed September 16, 2024. https://afribary.com/works/on-compact-operators-whose-norms-are-eigenvalues-and-completeness