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1.
Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that
have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more.
The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section
2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is
completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated
by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather
suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties
of completely irreducible operators are different from properties of unicellular operators.
__________
Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29 相似文献
2.
小球与均质自由杆的碰撞 总被引:2,自引:2,他引:0
讨论了小球与自由杆碰撞过程中所遵从的物理规律,明确了完全非弹性碰撞过程的能量特征,指出完全非弹性碰撞后两物体不一定粘在一起共同运动的事实. 相似文献
3.
§ 1 IntroductionA triple system of order v and indexλ,denoted by TS(v,λ) ,is a collection of3- ele-mentsubsets Aof a v- set X,so thatevery 2 - subsetof X appears in preciselyλ subsets of A.L etλ≥ 2 and (X,A) be a TS(v,λ) .If Acan be partitioned into t(≥ 2 ) parts A1,A2 ,...,Atsuch that each (X,Ai) is a TS(v,λi) for 1≤ i≤ t,then (X,A) is called de-composable.Otherwise it is indecomposable.If t=λ,λi=1for 1≤ i≤ t,the TS(v,λ) (X,A) is called completely decomposable.It … 相似文献
4.
We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BBT for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite). 相似文献
5.
We characterize δ-I-sets, discuss the relation between δ-sets, δ-I-sets and I
δ-sets and generalize some of the results. 相似文献
6.
I. Goba B. Turovska J. Stradins I. Turovskis E. Liepinsh S. Belyakov 《Chemistry of Heterocyclic Compounds》2007,43(2):175-186
It has been shown that chemical oxidation of the methyl ester of 3,4,5-trimethoxycarbonyl-1,2,6-trimethyl-1,4-dihydropyridine
to the pyridinium salt, requiring forcing experimental conditions, may be replaced by electrochemical oxidation. On electrochemical
reduction of 3,4,5-trimethoxycarbonyl-1,2,6-trimethylpyridinium perchlorate in the presence of alkylating agents 1,2,3,4,4,5,6-substituted
1,4-dihydropyridines are obtained.
__________
Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 226–237, February, 2007. 相似文献
8.
讨论了小球在杆上任一点的碰撞问题,并指出《大学物理》2006年第5期《小球与均质自由杆的碰撞》一文中"完全非弹性碰撞后两物体不一定粘在一起共同运动"的说法是错误的. 相似文献
9.
It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of topologicalradicals in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx. 相似文献
10.