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111.
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114.
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
115.
Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture
By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems. 相似文献
116.
Syntheses, structures, and properties of novel molybdenum and tungsten complexes of fullerenes 总被引:1,自引:0,他引:1
The synthesis and characterization of several fullerene-based organometallic complexes containing Mo and W is reported. 相似文献
117.
118.
On Dirichlet Characters of Polynomials 总被引:1,自引:0,他引:1
The main purpose of this paper is to use the properties of Gaussiansums and the analytic method to study the problem of calculatingone kind of character sums modulo q, and to give an interestingidentity. 2000 Mathematics Subject Classification 11L10, 11L40. 相似文献
119.
120.