Operator space structure of JC*-triples and TROs, I

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension

On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

Little G. T. for lp-lattice summing operators

2000 Mathematics Subject Classification: 46B28, 47D15.

On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

Operator, organizational, direct, and general support maintenance manual : heater, space, multi-fuel, with blower, 60,000 Btu/hr (Hunter model UH-68D), FSN 4520-114-1055.

"June 1969."

Operator, organizational, direct and general support maintenance manual : heater, space, multifuel, with blower, 15,000 BTU/hr, (Hunter model UH-48C, type I), NSN 4520-01-010-0316.

Includes index.

Operator, organizational, direct and general support maintenance manual : heater, space, multi-fuel, with blower, 60,000 BTU/hr, (Hunter model UH-68[[D), FSN 4520-114-1055.

"June 1969."

Operator, organizational, direct support and general support maintenance manual : heater, space, multifuel, with blower, 15,000 BTU/hr, 26 VDC, (Hunter model UH-48-C. type IV), NSN 4520-01-010-4059.

"August 1976."

Operator's, organizational, and direct support maintenance manual : heater, space, multifuel with blower, 15,000 BTU/hr, 28 VDC, (VBM model VBM 15-IV), NSN 4520-01-032-7363.

"21 September 1979."

Operator's, organizational, direct and general support maintenance manual : heater, space, multi-fuel, with blower, 60,000 BTU/HR, (Hunter model UH-68F), NSN 4520-01-050-5628.

Includes index.

Operator's, unit, and intermediate maintenance manual : heater, space, multifuel with blower, 60,000 Btu/hr, 120 V, UH-68G (4520-01-203-4410).

"4 November 1986."

Operator, organizational, and direct support maintenance manual including repair parts and special tools lists : heaters, space, radiant type, portable (type I, model M1941, solid fuel) FSN 4520-257-4877, (type II, model M1941, liquid fuel) FSN 4520-927-4214, (Yukon model M1950, solid or liquid fuel) FSN 4520-287-3353 : heaters, immersion, liquid fuel fired, for corrugated cans ....

"December 1969."

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.