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In this paper, we introduce the concept of sub-strongly maximal triangular algebras which form a large class of maximal triangular algebras, and prove that every algebraic isomorphism of sub-strongly maximal triangular algebras is spatially implemented, which generalizes the result by Ringrose in two respects.

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Fangyan Lu 《Proceedings of the American Mathematical Society》2007,135(8):2581-2590

We describe the structure of Lie derivations of -subspace lattice algebras. The results can apply to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras, respectively.

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Fangyan Lu 《Proceedings of the American Mathematical Society》2003,131(1):147-154

Let and be two nest algebras. A Jordan isomorphism from onto is a bijective linear map such that for every . In this note, we prove that every Jordan isomorphism of nest algebras is of the form or and then is, in fact, an isomorphism or an anti-isomorphism.

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Fangyan Lu 《Proceedings of the American Mathematical Society》2003,131(12):3883-3892

Let be a subalgebra of a nest algebra . If contains all rank one operators in , then is said to be large; if the set of rank one operators in coincides with that in the Jacobson radical of , is said to be radical-type. In this paper, algebraic isomorphisms of large subalgebras and of radical-type subalgebras are characterized. Let be a nest of subspaces of a Hilbert space and be a subalgebra of the nest algebra associated to (). Let be an algebraic isomorphism from onto . It is proved that is spatial if one of the following occurs: (1) () is large and contains a masa; (2) () is large and closed; (3) () is a closed radical-type subalgebra and ( is quasi-continuous (i.e. the trivial elements of are limit points); (4) () is large and one of and is not quasi-continuous.

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Abstract, In this paper, a necessary condition for a maximal triangular algebra to be closed is given, A necessary and sufficient condition for a maxima] triangular algebra to he strongly reducible is obtained, 相似文献

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A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles

*A*in , and that is a Jordan ideal if and only if it is an associative ideal. 相似文献9.

In the classical support vector machines, linear polynomials corresponding to the reproducing kernel

*K*(**x**,**y**)=**x****y**are used. In many models of learning theory, polynomial kernels*K*(**x**,**y**)=_{l=0}^{N}*a*_{l}(**x****y**)^{l}generating polynomials of degree*N*, and dot product kernels*K*(**x**,**y**)=_{l=0}^{+}*a*_{l}(**x****y**)^{l}are involved. For corresponding learning algorithms, properties of these kernels need to be understood. In this paper, we consider their positive definiteness. A necessary and sufficient condition for the dot product kernel*K*to be positive definite is given. Generally, we present a characterization of a function*f*:*R**R*such that the matrix [*f*(**x**^{i}**x**^{j})]_{i,j=1}^{m}is positive semi-definite for any**x**^{1},**x**^{2},...,**x**^{m}*R*^{n},*n*2. Supported by CERG Grant No. CityU 1144/01P and City University of Hong Kong Grant No. 7001342.AMS subject classification 42A82, 41A05 相似文献10.

Fangyan Lu 《Journal of Functional Analysis》2006,240(1):84-104

A Lie isomorphism

*?*between algebras is called trivial if*?*=*ψ*+*τ*, where*ψ*is an (algebraic) isomorphism or a negative of an (algebraic) anti-isomorphism, and*τ*is a linear map with image in the center vanishing on each commutator. In this paper, we investigate the conditions for the triviality of Lie isomorphisms from reflexive algebras with completely distributive and commutative lattices (CDCSL). In particular, we prove that a Lie isomorphism between irreducible CDCSL algebras is trivial if and only if it preserves*I*-idempotent operators (the sum of an idempotent and a scalar multiple of the identity) in both directions. We also prove the triviality of each Lie isomorphism from a CDCSL algebra onto a CSL algebra which has a comparable invariant projection with rank and corank not one. Some examples of Lie isomorphisms are presented to show the sharpness of the conditions. 相似文献