Linear and nonlinear variational inequalities on half-spaces
Linear approximation processes in locally convex spaces. I. Semigroups of operators and saturation.
Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space
2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94.New concepts of linear colligations and dynamic systems, corresponding to the linear operators, acting in the Banach spaces, are introduced. The main properties of the transfer function and its relation to the dual transfer function are established.
Linear complementarity problem and extremal hyperplanes
Linear contraction mappings
Linear elliptic operators with measurable coefficients
Linear Fractional PDE, Uniqueness of Global Solutions
Mathematics Subject Classification: 26A33, 47A60, 30C15.In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.
Linear fractional transformations and companion matrices
Linear independence in linear rings with abstract differentiation
Linear inessential operators and generalized inverses
The space of inessential bounded linear operators from one Banach space into another is introduced. This space, , is a subspace of which generalizes Kleinecke’s ideal of inessential operators. For certain subspaces of , it is shown that when has a generalized inverse modulo , then there exists a projection such that has a generalized inverse and .
Linear mappings preserving similarity on B(H)
Let H be an infinite-dimensional complex Hilbert space. We give a characterization of surjective linear mappings on B(H) that preserve similarity in both directions.
Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras
A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A),B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a 𝒥-subspace lattice ℒ on a Banach space X satisfying dim K ≠ 2 whenever K ∈ 𝒥(ℒ), every linear map on ℱ(ℒ) (the subalgebra of all finite rank operators in the JSL algebra Alg ℒ) Lie derivable at zero is of the standard form A ↦ δ (A) + ϕ(A), where δ is a generalized derivation and ϕ is a center-valued linear map. A characterization of linear maps Lie derivable...
Linear maps on Mₙ(ℂ) preserving the local spectral radius
Let x₀ be a nonzero vector in ℂⁿ. We show that a linear map Φ: Mₙ(ℂ) → Mₙ(ℂ) preserves the local spectral radius at x₀ if and only if there is α ∈ ℂ of modulus one and an invertible matrix A ∈ Mₙ(ℂ) such that Ax₀ = x₀ and for all T ∈ Mₙ(ℂ).
Linear maps preserving elements annihilated by the polynomial
Let H and K be complex complete indefinite inner product spaces, and ℬ(H,K) (ℬ(H) if K = H) the set of all bounded linear operators from H into K. For every T ∈ ℬ(H,K), denote by the indefinite conjugate of T. Suppose that Φ: ℬ(H) → ℬ(K) is a bijective linear map. We prove that Φ satisfies for all A, B ∈ ℬ(H) with if and only if there exist a nonzero real number c and a generalized indefinite unitary operator U ∈ ℬ(H,K) such that for all A ∈ ℬ(H).
Linear maps preserving quasi-commutativity
Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.
Linear maps preserving the generalized spectrum.
Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. For an operator T in B(H), let σg(T) denote the generalized spectrum of T. In this paper, we prove that if φ: B(H) → B(H) is a surjective linear map, then φ preserves the generalized spectrum (i.e. σg(φ(T)) = σg(T) for every T ∈ B(H)) if and only if there is A ∈ B(H) invertible such that either φ(T) = ATA-1 for every T ∈ B(H), or φ(T) = ATtrA-1 for every T ∈ B(H). Also, we...
Linear modulus of a multidimensional semigroup of -contractions and a differentiation theorem
Linear neutral partial differential equations: A semigroup approach.
Linear ODEs and -modules, solving and decomposing equations using symmetry methods.
Linear operators