Extension of stochastic dominance theory to random variables
Product of operators and numerical range preserving maps
Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of by . This includes the usual product and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying such that ϕ: V → V has the form A...
The joint essential numerical range of operators: convexity and related results
Let W(A) and be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A₁, ..., Aₘ) acting on an infinite-dimensional Hilbert space. It is shown that is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ 1, ..., m, can be obtained as the intersection of all sets of the form , where F = F* has finite rank. Moreover, the closure cl(W(A)) of W(A) is always star-shaped with the elements in as star centers....
Extension of stochastic dominance theory to random variables
In this paper, we develop some stochastic dominance theorems for the location and scale family and linear combinations of random variables and for risk lovers as well as risk averters that extend results in Hadar and Russell (1971) and Tesfatsion (1976). The results are discussed and applied to decision-making.
Jordan isomorphisms and maps preserving spectra of certain operator products
Let ₁, ₂ be (not necessarily unital or closed) standard operator algebras on locally convex spaces X₁, X₂, respectively. For k ≥ 2, consider different products on elements in , which covers the usual product and the Jordan triple product T₁ ∗ T₂ = T₂T₁T₂. Let Φ: ₁ → ₂ be a (not necessarily linear) map satisfying whenever any one of ’s has rank at most one. It is shown that if the range of Φ contains all rank one and rank two operators then Φ must be a Jordan isomorphism multiplied by a root...
Inequalities on the singular values of an off-diagonal block of a Hermitian matrix.
Shapes and computer generation of numerical ranges of Krein space operators.
Multiplicative maps on invertible matrices that preserve matricial properties.
Minimal distortion problems for classes of unitary matrices.
Maps preserving spectral radius, numerical radius, spectral norm.
Generalized numerical ranges of permanental compounds arising from quantum systems of bosons.
Numerical ranges of an operator on an indefinite inner product space.
Tracial numerical ranges and linear dependence of operators.
Euclidean and circum-Euclidean distance matrices: characterizations and linear preservers.
Spectral radius preservers of products of monnegative matrices.
Non-existence of full ray nonsingular matrices.
Shells of matrices in indefinite inner product spaces.
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