-negative matrices that define compact operators on a Banach sequence space. Math. Subj. Classification (2000): 47A10; 47B65; 47B07; 46A45. Key words: spectral radius, inequalities, infinite non-negative matrices, compact operators,

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An operator on a complex Banach space is polynomially compact if a non-zero polynomial of the operator is compact, and power compact if a power of the operator is compact. Theorems on triangularizability of algebras (resp. semigroups) of compact operators are shown to be valid also for algebras

In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a

sufficient conditions for a spectral algebra to have a nontrivial invariant subspace. When the associated operator is compact this leads to a generalization of V. Lomonosov’s theorem. 1.

We give an example of a Banach space X such thatK.X; X / is not an ideal inK.X; X/. We prove that if z is a weak denting point in the unit ball of Z and if X is a closed subspace of a Banach space Y, then the set of norm-preserving extensions HB.x⊗z / L.Z; Y / of a functional x⊗z 2.Z⊗X/ is equal to the set HB.x / ⊗ fzg. Using this result, we show that if X is an M-ideal in Y and Z is a

Abstract. We show examples of compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. This is the negative answer to an open question posed in the 1970’s. Actually, any strictly convex Banach space failing the approximation property serves

In this paper, it is shown that every compact operators are bounded and continuous. The bounded and continuous properties of an operator is sufficient for a Riesz operator. For mapping T: K- Iλ in normed linear space with some extended [1] properties, T becomes compact.

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