{"product_id":"axiomatic-spectral-theory-in-banach-algebras-von-raymond-lubansky","title":"Axiomatic Spectral Theory in Banach Algebras","description":"\u003cp\u003eIn Matrix Theory, the Spectral Mapping Theorem states  that for a matrix A and a polynomial p, {Eigenvalues  of p(A)} = p({Eigenvalues of A}). Spectral Theory  generalises eigenvalues, invertibility and the  spectral mapping theorem to Banach algebras.  Axiomatic Spectral Theory takes this a step further  to pseudo-invertibility and considers the associated  spectral mapping theorem which has applications in  various areas such as differential equations. This  book develops a new pointwise axiomatic theory based on Muller''s Regularites, sharing and extending  several properties. The spectral mapping theorem is  proved and extended to pointwise theory. Other forms  of axiomatic spectra are shown to form Total  Pointwise Regularities. Many sets are shown to have  good spectral properties and some new sets are shown  to be Global Regularities. The derived approach of  Berkani''s regularity theory is developed and  axiomatised into a restricted theory that will always  lead to a global regularity. Also, the systematic  approach to regularities of Mbekhta and Muller are  examined and extended to general Banach algebras by  means of annihilators and the socle.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838350974\"\u003e\u003ch3\u003eA generalisation of Regularity Theory in Banach Algebras to Pointwise Regularity Theory and  applications\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838350974","offer_id":39498961027165,"sku":"9783838350974","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/4179ebf9-03f3-4d3e-8faf-118e4e06b55c.jpg?v=1770703146","url":"https:\/\/shop.autorenwelt.de\/products\/axiomatic-spectral-theory-in-banach-algebras-von-raymond-lubansky","provider":"Autorenwelt Shop","version":"1.0","type":"link"}