Let V n(q) be the n dimensional vector space over the finite field with q elements, K a k dimensional subspace and C the set of the subspaces S such that S∩K≠=O .We show that C ...Let V n(q) be the n dimensional vector space over the finite field with q elements, K a k dimensional subspace and C the set of the subspaces S such that S∩K≠=O .We show that C is Sperner and unimodal and point out all maximum sized antichains in C .For the Whitney number W m of C , we show that W m 2 qW m 1 W m+1 has nonnegative coefficients as a polynomial in q and that W 0W nW 1W n 1 W 2… .展开更多
Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C...Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C-derivations and C-derivations at zero point on Alg：D are generalized Ф-derivations.展开更多
In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivi...In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity,automorphism and finite rank operators.展开更多
Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B...Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.展开更多
If K ∩ AlgL is weak. dense in AlgL, where K is the set of all compactoperators in B(H), is completely distributive? In this note, we prove that there is a reflexivesubspace lattice L on some Hilbert space, which sati...If K ∩ AlgL is weak. dense in AlgL, where K is the set of all compactoperators in B(H), is completely distributive? In this note, we prove that there is a reflexivesubspace lattice L on some Hilbert space, which satisfies the following conditions: (a) F(AlgL) isdense in AlgL in the ultrastrong operator topology, where F(AlgL) is the set of all finite rankoperators in AlgL; (b) L isnt a completely distributive lattice. The subspace lattices that satisfythe above conditions form a large class of lattices. As a special case of the result, it easy to seethat the answer to Problem 7 is negative.展开更多
文摘Let V n(q) be the n dimensional vector space over the finite field with q elements, K a k dimensional subspace and C the set of the subspaces S such that S∩K≠=O .We show that C is Sperner and unimodal and point out all maximum sized antichains in C .For the Whitney number W m of C , we show that W m 2 qW m 1 W m+1 has nonnegative coefficients as a polynomial in q and that W 0W nW 1W n 1 W 2… .
基金Supported by the National Natural Science Foundation of China (Grant No.10871224)the Natural Science Young Foundation of Shaanxi Province (Grant No.2010JQ1003)+1 种基金the Natural Science Special Foundation of Education Department of Shaanxi Province (Grant No.08JK344)the Basic Research Foundation of Xi'an University of Architecture and Technology (Grant No.JC1009)
文摘Let D= {{0},/4, L, M, X} be a strongly double triangle subspace lattice on a nonzero complex reflexive Banach space X, which satisfies that one of three sums K ＋ L, L＋M and M ＋ K is closed. It is shown that local C-derivations and C-derivations at zero point on Alg：D are generalized Ф-derivations.
文摘In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity,automorphism and finite rank operators.
基金Supported by National Natural Foundation of China(11001194)Provincial International Cooperation Project of Shanxi(2014081027-2)
文摘Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.
文摘If K ∩ AlgL is weak. dense in AlgL, where K is the set of all compactoperators in B(H), is completely distributive? In this note, we prove that there is a reflexivesubspace lattice L on some Hilbert space, which satisfies the following conditions: (a) F(AlgL) isdense in AlgL in the ultrastrong operator topology, where F(AlgL) is the set of all finite rankoperators in AlgL; (b) L isnt a completely distributive lattice. The subspace lattices that satisfythe above conditions form a large class of lattices. As a special case of the result, it easy to seethat the answer to Problem 7 is negative.
