Principles of Functional Analysis

Schechter, Martin

doi:10.1090/gsm/036

Cited by 173 publications

(176 citation statements)

References 0 publications

Supporting

Mentioning

176

Contrasting

Order By: Relevance

“…The proof relies on the Banach-Steinhaus principle. Under the stronger hypothesis that both X and Y are Banach, it is stated as an exercise in Schechter's book [15,Exercise 24,p. 74].…”

Section: Introductionmentioning

confidence: 99%

Compact bilinear operators and commutators

Bényi

Torres

2013

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…The proof relies on the Banach-Steinhaus principle. Under the stronger hypothesis that both X and Y are Banach, it is stated as an exercise in Schechter's book [15,Exercise 24,p. 74].…”

Section: Introductionmentioning

confidence: 99%

Compact bilinear operators and commutators

Bényi

Torres

2013

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…This implies that A † and A −1 are bounded operators, and the following identities are satisfied [17,14].…”

Section: −1mentioning

confidence: 99%

Is weak pseudo-Hermiticity weaker than pseudo-Hermiticity?

Mostafazadeh¹

2006

Journal of Mathematical Physics

View full text Add to dashboard Cite

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltonian is selected from among these operators correspond to pseudo-Hermitian quantum systems possessing certain symmetries.PACS number: 03.65.-w

show abstract

“…The subsets σ e1,I (·) and σ e2,I (·) are the Gustafson and Weidmann essential spectra [2], σ e3,I (·) is the Kato essential spectrum [15], σ e4,I (·) is the Wolf essential spectrum [2-5, 9, 25, 26], σ e5,I (·) is the Schechter essential spectrum [2,[6][7][8][9]20,21], σ e6,I (·) denotes the Browder essential spectrum [2,9,10,13,18], σ e7,I (·) was introduced by V. Rakocević in [19] and designates the essential approximate point spectrum and σ e8,I (·) is the essential defect spectrum and was introduced by V. Schmoeger [23].…”

Section: Kato Operator If R(a) Is Closed and Nmentioning

confidence: 99%