Sous-espaces invariants d'un opérateur nilpotent sur un espace de banach

Barraa, Mohamed; Charles, Bernard

doi:10.1016/0024-3795(91)90217-k

Cited by 7 publications

(3 citation statements)

References 2 publications

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“…The theorem above provides a coarse structure for Hlat(T), especially when this lattice is infinite. This result also extends the main theorem in [3], and it represents a slight improvement even in the nilpotent case.…”

Section: Theorem 73 Let T ∈ L(h) Be An Arbitrary Operator M ∈ Hlat(supporting

confidence: 83%

“…The hyperlattice of Herrero's operator is still generated by the subspaces ker T m and (ran T m ) − for m = 0, 1, 2, 3. In fact Herrero conjectured (see especially his review of [3]) that Hlat(T) is always generated by ker T m and (ran T m ) − if T is nilpotent and therefore T has a smallest and a largest nontrivial hyperinvariant subspace. The latter statement is in fact true, as shown by the following result of Barraa [3].…”

Section: Proposition 52 If Two Generalized Jordan Operators Are Hypementioning

confidence: 99%

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On the Hyperinvariant Subspace Problem. IV

Bercovici¹,

Foiaş²,

Pearcy³

2008

Can. j. math.

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Abstract. This paper is a continuation of three recent articles concerning the structure of hyperinvariant subspace lattices of operators on a (separable, infinite dimensional) Hilbert space H. We show herein, in particular, that there exists a "universal" fixed block-diagonal operator B on H such that if ε > 0 is given and T is an arbitrary nonalgebraic operator on H, then there exists a compact operator K of norm less than ε such that (i) Hlat(T) is isomorphic as a complete lattice to Hlat(B + K) and (ii) B + K is a quasidiagonal, C 00 , (BCP)-operator with spectrum and left essential spectrum the unit disc. In the last four sections of the paper, we investigate the possible structures of the hyperlattice of an arbitrary algebraic operator. Contrary to existing conjectures, Hlat(T) need not be generated by the ranges and kernels of the powers of T in the nilpotent case. In fact, this lattice can be infinite.

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Section: Theorem 73 Let T ∈ L(h) Be An Arbitrary Operator M ∈ Hlat(supporting

confidence: 83%

Section: Proposition 52 If Two Generalized Jordan Operators Are Hypementioning

confidence: 99%

On the Hyperinvariant Subspace Problem. IV

Bercovici¹,

Foiaş²,

Pearcy³

2008

Can. j. math.

View full text Add to dashboard Cite

show abstract

“…The conjecture is true at least for the case where T is similar to a Jordan model [76]. Bernard and Josette Charles, and their students M. Barraa and M. El Oufir [28,15,46], have recently made some progress toward an affirmative answer to the above conjecture.…”

Section: If Te^(j^) Is Algebraic With Minimal Polynomial P Then Hypementioning

confidence: 99%