scholarly journals An elementary proof of a fundamental theorem in the theory of Banach algebras.

1958 ◽  
Vol 5 (1) ◽  
pp. 75-78 ◽  
Author(s):  
C. E. Rickart
Keyword(s):  
Fundamental Theorem ◽  
Elementary Proof ◽  
Banach Algebras

scholarly journals A characterization of Banach-star-algebras by numerical range

1971 ◽  
Vol 4 (2) ◽  
pp. 193-200 ◽  
Author(s):  
Brailey Sims
Keyword(s):  
Elementary Proof ◽  
Numerical Range ◽  
Banach Algebras

It is known that in a B*-algebra every self-adjoint element is hermitian. We give an elementary proof that this condition characterizes B*-algetras among Banach*-algebras.

scholarly journals Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras

1995 ◽  
Vol 2 (4) ◽  
pp. 425-444
Author(s):  
Jean Marion ◽  
Thierry Robart
Keyword(s):  
Differential Geometry ◽  
Lie Groups ◽  
Wide Class ◽  
Fundamental Theorem ◽  
Banach Algebras ◽  
Inverse Limits ◽  
Topological Algebras ◽  
Infinite Dimensional ◽  
Dimensional Version ◽  
Invertible Elements

Abstract We consider a wide class of unital involutive topological algebras provided with a C*-norm and which are inverse limits of sequences of unital involutive Banach algebras; these algebras are taking a prominent position in noncommutative differential geometry, where they are often called unital smooth algebras. In this paper we prove that the group of invertible elements of such a unital solution smooth algebra and the subgroup of its unitary elements are regular analytic Fréchet–Lie groups of Campbell–Baker–Hausdorff type and fulfill a nice infinite-dimensional version of Lie's second fundamental theorem.

scholarly journals An Elementary Proof of the Hook Formula

10.37236/769 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Jason Bandlow
Keyword(s):  
Fundamental Theorem ◽  
Elementary Proof ◽  
Young Tableaux ◽  
Hook Length ◽  
Inductive Approach ◽  
Fundamental Theorem Of Algebra ◽  
Hook Formula

The hook-length formula is a well known result expressing the number of standard tableaux of shape $\lambda$ in terms of the lengths of the hooks in the diagram of $\lambda$. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing more than the fundamental theorem of algebra. This proof was suggested by a $q,t$-analog of the hook formula given by Garsia and Tesler, and is roughly based on the inductive approach of Greene, Nijenhuis and Wilf. We also prove the hook formula in the case of shifted Young tableaux using the same technique.

XVIII.—The Elementary Proof of the Prime Number Theorem

1952 ◽  
Vol 63 (3) ◽  
pp. 257-267 ◽  
Author(s):  
E. M. Wright
Keyword(s):  
Prime Number ◽  
Fundamental Theorem ◽  
Elementary Proof ◽  
Prime Number Theorem ◽  
Integral Calculus ◽  
Basic Ideas ◽  
Fundamental Theorem Of Arithmetic ◽  
Theory Of Numbers

SynopsisThe author presents a modification of the recently discovered “elementary” proof of the Prime Number Theorem. Nothing is assumed from the theory of numbers except the Fundamental Theorem of Arithmetic. In the second part of the proof the elements of the integral calculus are used to make clearer the basic ideas on which this part depends.

AN ELEMENTARY PROOF OF A THEOREM OF LEE

1991 ◽  
Vol 11 (3) ◽  
pp. 356-360 ◽  
Author(s):  
Jia'an Yan
Keyword(s):  
Elementary Proof
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