Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

2000 Mathematics Subject Classification: Primary 43A22, 43A25.

Multipliers on a Hilbert Space of Functions on R

2000 Mathematics Subject Classification: 42A45.

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

Vaughan, Suzi and Armstrong, Wendy (2009) Threads of tension. In: Vaughan, Suzi and Schmidt, Christine Margaret, (eds.) Five Fashion Musings. Post Pressed, Brisbane, Qld, pp. 9-15.

five:fashion musings is an upcoming 2009 publicaton to celebrate the fashion discipline's five-year milestone at the Queensland Unviesity of Technology. it represents a body of work by fashion practitioners, aceademic and educators commissioned to explore their research in fashion theory, practice and pedogogy through five key themes.