Results 1  10
of
9,113
Triangularizability of Polynomially Compact Operators
"... An operator on a complex Banach space is polynomially compact if a nonzero 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 (res ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
An operator on a complex Banach space is polynomially compact if a nonzero 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
Singular traces and compact operators
 J. Funct. Anal
, 1996
"... 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 nonzero value on T. This generalizes previous results by Dixmier and Varga. We also give an explicit descri ..."
Abstract

Cited by 22 (10 self)
 Add to MetaCart
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 nonzero value on T. This generalizes previous results by Dixmier and Varga. We also give an explicit
COMPACT OPERATORS AND THE SCHRÖDINGER EQUATION
, 2006
"... 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 basis ..."
Abstract
 Add to MetaCart
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
On the Functional Inequality . . . OF COMPACT OPERATORS
, 2009
"... In [6], Elsner, Hershkowitz and Pinkus characterized functions F: IR n + → IR+ satisfying r(F (A1,..., An)) ≤ F (r(A1),..., r(An)) for all nonnegative matrices A1,..., An of the same order, where r denotes the spectral radius. We generalize this result to the setting of infinite nonnegative mat ..."
Abstract
 Add to MetaCart
negative matrices that define compact operators on a Banach sequence space.
Beyond hyperinvariance for compact operators
 J. Funct. Anal
"... Abstract. We introduce a new class of operator algebras on Hilbert space. To each bounded linear operator a spectral algebra is associated. These algebras are quite substantial, each containing the commutant of the associated operator, frequently as a proper subalgebra. We establish several sufficie ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
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.
IDEALS OF COMPACT OPERATORS
 J. AUST. MATH. SOC. 77 (2004), 91–110
, 2004
"... 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 normpreserving extensions HB.x⊗z / L.Z; Y / of a functional x⊗z 2.Z⊗X/ is equa ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
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 normpreserving 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 Mideal in Y and Z is a
About Riesz theory of compact operators
"... 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
 Add to MetaCart
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.
Normattaining compact operators
"... 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 as th ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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
NORMATTAINING COMPACT OPERATORS
"... 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 as the rang ..."
Abstract
 Add to MetaCart
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
Results 1  10
of
9,113