Abstract not found

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

We give a necessary and sufficient condition on a positive compact operator T for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on T. This generalizes previous results by Dixmier and Varga. We also give an explicit

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

-negative matrices that define compact operators on a Banach sequence space.

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

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.

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

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