The Bishop–Phelps–Bollobás properties in complex Hilbert spaces

Yun Sung Choi, Sheldon Dantas, Mingu Jung

Type: Article

Publication Date: 2021-11-01

Citations: 3

DOI: https://doi.org/10.1002/mana.201900288

Abstract

Abstract In this paper, we consider the Bishop–Phelps–Bollobás point property for various classes of operators on complex Hilbert spaces, which is a stronger property than the Bishop–Phelps–Bollobás property. We also deal with analogous problem by replacing the norm of an operator with its numerical radius.

Locations

arXiv (Cornell University) - View - PDF
Repositori UJI (Universitat Jaume I) - View - PDF
Mathematische Nachrichten - View

Similar Works

Action	Title	Year	Authors
+	Some remarks on the Bishop-Phelps-Bollob\'as property in complex Hilbert spaces	2018	Yun Sung Choi Sheldon Dantas Mingu Jung
+	The Bishop-Phelps-Bollobás properties in complex Hilbert spaces	2018	Yun Sung Choi Sheldon Dantas Mingu Jung
+	On the Bishop-Phelps-Bollobás type theorems	2017	Sheldon Dantas
+ PDF Chat	The Bishop–Phelps–Bollobás Property: a Finite-Dimensional Approach	2015	Marı́a D. Acosta Julio Becerra Guerrero Domingo Garcı́a Sun Kwang Kim Manuel Maestre
+	The Bishop–Phelps–Bollobás property for numerical radius on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>	2014	Javier Falcó
+ PDF Chat	On the Compact Operators Case of the Bishop–Phelps–Bollobás Property for Numerical Radius	2021	Domingo Garcı́a Manuel Maestre Miguel Martı́n Óscar Roldán
+ PDF Chat	The Bishop–Phelps–Bollobás property for operators on $\mathcal{C}(K)$	2016	Marı́a D. Acosta
+	On the compact operators case of the Bishop-Phelps-Bollobás property for numerical radius	2021	Domingo Garcı́a Manuel Maestre Miguel Martı́n Óscar Roldán
+	THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES	2013	Domingo Garcı́a Manuel Maestre Han Ju Lee
+	On the compact operators case of the Bishop-Phelps-Bollob\'as property for numerical radius	2021	Domingo Garcı́a Manuel Maestre Miguel Martı́n Óscar Roldán
+	On the Bishop-Phelps theorem in Complex spaces	2000	Victor Lomonosov
+	The Bishop–Phelps–Bollobás property for numerical radius of operators on L1(μ)	2017	Marı́a D. Acosta M. Fakhar Maryam Soleimani-Mourchehkhorti
+	The Bishop-Phelps-Bollobas Theorem and operators on Banach spaces	2014	Olena Kozhushkina
+	The Bishop-Phelps-Bollobás property for compact operators	2016	Sheldon Dantas Domingo Garcı́a Manuel Maestre Miguel Martı́n
+	Local Bishop–Phelps–Bollobás properties	2018	Sheldon Dantas Sun Kwang Kim Han Ju Lee Martín Mazzitelli
+	The Bishop-Phelps-Bollob\'as property for compact operators	2016	Sheldon Dantas Domingo Garcı́a Manuel Maestre Miguel Martı́n
+	A note on Bishop-Phelps-Bollobás theorem for operators	2022	T. Grando Mary Lilian Lourenço
+	The Bishop-Phelps-Bollob\'as point property	2016	Sheldon Dantas Sun Kwang Kim Han Ju Lee
+	The strong Bishop-Phelps-Bollobás property	2016	Sheldon Dantas
+	The Bishop–Phelps–Bollobás theorem for operators	2008	Marı́a D. Acosta Richard M. Aron Domingo Garcı́a Manuel Maestre

Works That Cite This (3)

Action	Title	Year	Authors
+	The Bishop–Phelps–Bollobás Theorem: An Overview	2022	Sheldon Dantas Domingo Garcı́a Manuel Maestre Óscar Roldán
+ PDF Chat	Norm-attaining operators which satisfy a Bollobás type theorem	2021	Sheldon Dantas Mingu Jung Óscar Roldán
+ PDF Chat	On various types of density of numerical radius attaining operators	2023	Sheldon Dantas Sun Kwang Kim Han Ju Lee Martín Mazzitelli

Works Cited by This (34)

Action	Title	Year	Authors
+	Denseness of norm attaining mappings	2006	María Dolores Acosta Vigil
+	Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras	1971	F. F. Bonsall John F. R. Duncan
+	Compact non-self-adjoint operators	1971	J. R. Ringrose
+ PDF Chat	Numerical radius-attaining operators on 𝐶(𝐾)	1985	Carmen Silvia Cardassi
+ PDF Chat	On numerical range and its application to Banach algebras	1972	Brailey Sims
+ PDF Chat	Denseness of operators which attain their numerical radius	1984	Ina Berg Brailey Sims
+	Numerical Radius Attaining Operators and the Radon-Nikodym Property	1993	Marı́a D. Acosta Rafael Payá
+	The Bishop–Phelps–Bollobás property for numerical radius on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>	2014	Javier Falcó
+ PDF Chat	A proof that every Banach space is subreflexive	1961	Errett Bishop R. R. Phelps
+ PDF Chat	On the Bishop-Phelps-Bollobás Property for Numerical Radius	2014	Sun Kwang Kim Han Ju Lee Miguel Martı́n