On Small Subspace Lattices in Hilbert Space

Aiju, Dong; Wu, Wenming; Yuan, Wei

doi:10.1017/s1446788713000384

Cited by 5 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…首先注意到当两个投影 P 和 Q 满足 P ∧ Q = 0 和 P ∨ Q = I 时, 它们将具有如下算子矩阵形式. 引理 2.1 [21] 假设 P 和 Q 是 H 上的投影算子. 证明设 (I − Q) ∧ P = 0.…”

Section: 两个投影算子构成的算子组的联合谱unclassified

The joint spectrum of a tuple of projections

Wu¹,

Yecong²,

Ruan³

et al. 2020

Sci. Sin.-Math.

View full text Add to dashboard Cite

We study the joint spectrum of projections in a Hilbert space, and calculate the joint spectrum of a pair of projections. In particular, by calculating the joint spectrum for a tuple [I, P, Q] in which I is the identity and P , Q is a regular pair of projections, we get specific characterizations of the spectrums of P + Q and P − Q, respectively. Conversely, we prove that two closed subsets of C in particular forms are respectively the spectrums of the sum and the difference of a regular pair of projections. We also calculate the joint spectrum of a 3-tuple of projections [P, Q, R] for P , Q and R satisfying some specific conditions.

show abstract

Section: 两个投影算子构成的算子组的联合谱unclassified

The joint spectrum of a tuple of projections

Wu¹,

Yecong²,

Ruan³

et al. 2020

Sci. Sin.-Math.

View full text Add to dashboard Cite

show abstract

“…A pentagon subspace lattice can be refelexive or non-reflexive, while for the double triangle subspace lattices no reflexive example is known. Pentagon and double triangle subspace lattices have been studied in [4,6,15,24].…”

Section: Introductionmentioning

confidence: 99%

Reflexive sets of operators

Bračič¹,

Diogo²,

Zając³

2018

Banach J. Math. Anal.

View full text Add to dashboard Cite

In this survey paper we present known results about reflexive subspace lattices. We show that every nest and every atomic Boolean subspace lattice in a complex Banach space is reflexive, even strongly reflexive. Our main tool is Ringrose's Lemma about presence of rank-one operators in a reflexive algebra of operators. We consider realizations of small lattices as subspace lattices in Banach spaces. We exhibit some realizations of the pentagon and prove that some of these realizations are reflexive. On the other hand, we show that double triangle subspace lattices in finite-dimensional Banach spaces are non-reflexive.

show abstract

On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice

Aiju

Wang

2015

Sci. China Math.

Self Cite

View full text Add to dashboard Cite

We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M (with L = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L) * . Our method can be used to prove similar results in finite-dimensional matrix algebras. As a consequence, we give a new proof to the main theorem by Hou and Zhang (2012). KeywordsKadison-Singer algebra, Kadison-Singer lattice, reflexive algebra, double triangle lattice, factor of type II 1 MSC(2010) 47L35, 47L75, 46L10Citation: Dong A J, Wang D. On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice.

show abstract

On Small Subspace Lattices in Hilbert Space

Cited by 5 publications

References 19 publications

The joint spectrum of a tuple of projections

The joint spectrum of a tuple of projections

Reflexive sets of operators

On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice

Contact Info

Product

Resources

About