Diptesh Saha | Presidency University, Kolkata (original) (raw)

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Papers by Diptesh Saha

Research paper thumbnail of On the non-commutative Neveu decomposition and stochastic ergodic theorems

arXiv (Cornell University), Aug 25, 2023

In this article, we prove Neveu decomposition for the action of locally compact amenable semigrou... more In this article, we prove Neveu decomposition for the action of locally compact amenable semigroup of positive contractions on semifinite von Neumann algebras and thus, it entirely resolves the problem for the actions of arbitrary amenable semigroup on semifinite von Neumann algebras. We also prove it for amenable group actions by Markov automorphisms on any σ-finite von Neumann algebras. As an application, we obtain stochastic ergodic theorem for actions of Z d + and R d + for d ∈ N by positive contractions on L 1-spaces associated with a finite von Neumann algebra. It yields the first ergodic theorem for positive contraction on non-commutative L 1-spaces beyond the Danford-Schwartz category.

Research paper thumbnail of On noncommutative ergodic theorems for semigroup and free group actions

arXiv (Cornell University), Jul 2, 2023

In this article, we consider actions of Z d + , R d + and finitely generated free groups on a von... more In this article, we consider actions of Z d + , R d + and finitely generated free groups on a von Neumann algebras M and prove a version of maximal ergodic inequality. Additionally, we establish non-commutative analogues of pointwise ergodic theorems for associated actions in the predual when M is finite.

Research paper thumbnail of On the non-commutative Neveu decomposition and ergodic theorems for amenable group action

Journal of Functional Analysis

Research paper thumbnail of Tendency Message Implementation of Competitive Identity Nation Branding: Wonderful Indonesia

Since 2010, Indonesia has announced a nation brand: Wonderful Indonesia which was declared by the... more Since 2010, Indonesia has announced a nation brand: Wonderful Indonesia which was declared by the Ministry of Tourism as a tourism branding nation in Indonesia. This research takes the Ministry of Tourism and Creative Economy on Instagram @parekraf which has published information to the public as a form of publication of nation branding: Wonderful Indonesia. In the process, this research uses quantitative research methods of content analysis. This research was conducted in September-November 2019 which showed a valid agreement among coders and analysis results where the largest percentage was in the caption and image analysis unit namely the element of tourism promotion (tourism promotion) where the caption was 61.4% and the figure was 57%. The element that has the lowest percentage is exporting brands at 0% in each unit of analysis. The other elements are society by 3.5% in the caption and 8.7% in the image, culture 0% in the caption and 7% in the image, investment 29% in the caption and 22% in the image, and policy on a caption of 3.5% in each unit of analysis. Research suggests that the percentage of culture (exporting culture) and exporting brands should be stronger because it is a important element in representing nation branding.

Research paper thumbnail of On the von Neumann algebras associated to Yang–Baxter operators

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020

Bożejko and Speicher associated a finite von Neumann algebra M T to a self-adjoint operator T on ... more Bożejko and Speicher associated a finite von Neumann algebra M T to a self-adjoint operator T on a complex Hilbert space of the form mathcalHotimesmathcalH\mathcal {H}\otimes \mathcal {H}mathcalHotimesmathcalH which satisfies the Yang–Baxter relation and $ \left\| T \right\| < 1$ . We show that if dim (mathcalH)(\mathcal {H})(mathcalH) ⩾ 2, then M T is a factor when T admits an eigenvector of some special form.

Research paper thumbnail of On the non-commutative Neveu decomposition and stochastic ergodic theorems

arXiv (Cornell University), Aug 25, 2023

In this article, we prove Neveu decomposition for the action of locally compact amenable semigrou... more In this article, we prove Neveu decomposition for the action of locally compact amenable semigroup of positive contractions on semifinite von Neumann algebras and thus, it entirely resolves the problem for the actions of arbitrary amenable semigroup on semifinite von Neumann algebras. We also prove it for amenable group actions by Markov automorphisms on any σ-finite von Neumann algebras. As an application, we obtain stochastic ergodic theorem for actions of Z d + and R d + for d ∈ N by positive contractions on L 1-spaces associated with a finite von Neumann algebra. It yields the first ergodic theorem for positive contraction on non-commutative L 1-spaces beyond the Danford-Schwartz category.

Research paper thumbnail of On noncommutative ergodic theorems for semigroup and free group actions

arXiv (Cornell University), Jul 2, 2023

In this article, we consider actions of Z d + , R d + and finitely generated free groups on a von... more In this article, we consider actions of Z d + , R d + and finitely generated free groups on a von Neumann algebras M and prove a version of maximal ergodic inequality. Additionally, we establish non-commutative analogues of pointwise ergodic theorems for associated actions in the predual when M is finite.

Research paper thumbnail of On the non-commutative Neveu decomposition and ergodic theorems for amenable group action

Journal of Functional Analysis

Research paper thumbnail of Tendency Message Implementation of Competitive Identity Nation Branding: Wonderful Indonesia

Since 2010, Indonesia has announced a nation brand: Wonderful Indonesia which was declared by the... more Since 2010, Indonesia has announced a nation brand: Wonderful Indonesia which was declared by the Ministry of Tourism as a tourism branding nation in Indonesia. This research takes the Ministry of Tourism and Creative Economy on Instagram @parekraf which has published information to the public as a form of publication of nation branding: Wonderful Indonesia. In the process, this research uses quantitative research methods of content analysis. This research was conducted in September-November 2019 which showed a valid agreement among coders and analysis results where the largest percentage was in the caption and image analysis unit namely the element of tourism promotion (tourism promotion) where the caption was 61.4% and the figure was 57%. The element that has the lowest percentage is exporting brands at 0% in each unit of analysis. The other elements are society by 3.5% in the caption and 8.7% in the image, culture 0% in the caption and 7% in the image, investment 29% in the caption and 22% in the image, and policy on a caption of 3.5% in each unit of analysis. Research suggests that the percentage of culture (exporting culture) and exporting brands should be stronger because it is a important element in representing nation branding.

Research paper thumbnail of On the von Neumann algebras associated to Yang–Baxter operators

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020

Bożejko and Speicher associated a finite von Neumann algebra M T to a self-adjoint operator T on ... more Bożejko and Speicher associated a finite von Neumann algebra M T to a self-adjoint operator T on a complex Hilbert space of the form mathcalHotimesmathcalH\mathcal {H}\otimes \mathcal {H}mathcalHotimesmathcalH which satisfies the Yang–Baxter relation and $ \left\| T \right\| < 1$ . We show that if dim (mathcalH)(\mathcal {H})(mathcalH) ⩾ 2, then M T is a factor when T admits an eigenvector of some special form.

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