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[3] viXra:2410.0113 [pdf] submitted on 2024-10-19 01:51:57
Authors: Guo Shile, Huanyin Chen
Comments: 15 Pages.
In this article, we present novel additive properties for the g-Drazin inverse within the context of Banach algebras. Subsequently, we provide representations for the g-Drazin inverse of block operator matrices defined over Banach spaces. These findings build upon and extend various well-known results, such as those by Bu, Feng, and Bai (J. Comput. Appl. Math., 218(2012), 10226--10237) and Dopazo and Martínez-Serrano (Linear Algebra Appl., 432(2010), 1896--1904).
Category: Algebra
[2] viXra:2410.0104 [pdf] submitted on 2024-10-18 20:00:24
Authors: Guo Shilu, Huanyin Chen
Comments: 21 Pages. In Chinese
In this paper, we investigate the p-Drazin inverse of the anti-triangular operator matrix $left(begin{array}{cc} a & 1 b & 0 end{array} ight)$. We identify two new class of necessary and sufficient conditions for an anti-triangular matrix to possess a p-Drazin inverse. Subsequently, we generalize several established results to a broader context. As practical applications, we demonstrate the p-Drazin invertibility of specific block operator matrices $left( begin{array}{cc} A & B C & D end{array}ight)in mathcal{B}(Xoplus X)$.
Category: Algebra
[1] viXra:2410.0036 [pdf] replaced on 2025-02-04 19:01:47
Authors: Makafui Apedo
Comments: 12 Pages.
If mathematics is a language, then African American Vernacular English (AAVE) or Ebonics as its generally known holds the key to understanding the evolution of Algebra from human speech in North America. The use of the slang sumthin to depict an unknown amount of money that varies implies that Algebra developed as a logical necessity in human communication. Exploring this phenomenon and leveraging it to demonstrate the concept of Algebra can enhance the comprehension of the subject among speakers of AAVE.
Category: Algebra
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