Polar Decompositions in Finite Dimensional Indefinite Scalar Product Spaces: Special Cases and Applications

1996 ◽  
pp. 61-94 ◽  
Author(s):  
Yuri Bolshakov ◽  
Cornelis V. M. van der Mee ◽  
André C. M. Ran ◽  
Boris Reichstein ◽  
Leiba Rodman
Keyword(s):  
Scalar Product ◽  
Product Spaces ◽  
Finite Dimensional ◽  
Special Cases

scholarly journals Errata for: Polar decomposition in finite dimensional indefinite scalar product spaces: Special cases and applications

1997 ◽  
Vol 27 (4) ◽  
pp. 497-501 ◽  
Author(s):  
Yuri Bolshakov ◽  
Cornelis V. M. van der Mee ◽  
André C. M. Ran ◽  
Boris Reichstein ◽  
Leiba Rodman
Keyword(s):  
Scalar Product ◽  
Polar Decomposition ◽  
Product Spaces ◽  
Finite Dimensional ◽  
Special Cases

scholarly journals Polar decompositions in finite dimensional indefinite scalar product spaces: General theory

1997 ◽  
Vol 261 (1-3) ◽  
pp. 91-141 ◽  
Author(s):  
Yuri Bolshakov ◽  
Cornelis V.M. van der Mee ◽  
AndréC.M. Ran ◽  
Boris Reichstein ◽  
Leiba Rodman
Keyword(s):  
General Theory ◽  
Scalar Product ◽  
Product Spaces ◽  
Finite Dimensional

scholarly journals Classes of plus matrices in finite dimensional indefinite scalar product spaces

1998 ◽  
Vol 30 (4) ◽  
pp. 432-451 ◽  
Author(s):  
Cornelis V. M. van der Mee ◽  
André C. M. Ran ◽  
L. Rodman
Keyword(s):  
Scalar Product ◽  
Product Spaces ◽  
Finite Dimensional

Extension of Isometries in Finite-Dimensional Indefinite Scalar Product Spaces and Polar Decompositions

1997 ◽  
Vol 18 (3) ◽  
pp. 752-774 ◽  
Author(s):  
Yuri Bolshakov ◽  
Cornelis V. M. van der Mee ◽  
André C. M. Ran ◽  
Boris Reichstein ◽  
Leiba Rodman
Keyword(s):  
Scalar Product ◽  
Product Spaces ◽  
Finite Dimensional ◽  
Extension Of Isometries

scholarly journals A note on liftings of hermitian elements and unitaries

1980 ◽  
Vol 21 (1) ◽  
pp. 183-185
Author(s):  
C. K. Fong
Keyword(s):  
Banach Algebra ◽  
Present Note ◽  
Partial Answer ◽  
General Question ◽  
Quotient Mapping ◽  
Unitary Element ◽  
Finite Dimensional ◽  
Complex Banach Algebra ◽  
Special Cases

Let A be a complex Banach algebra with unit 1 satisfying ∥1∥ = 1. An element u in A is said to be unitary if it is invertible and ∥u∥ = ∥u−1∥ = 1. An element h in A is said to be hermitian if ∥exp(ith)∥ = 1 for all real t; that is, exp(ith) is unitary for all real t. Suppose that J is a closed two-sided ideal and π: A → A/J is the quotient mapping. It is easy to see that if x in A is hermitian (resp. unitary), then so is π(x) in A/J. We consider the following general question which is the converse of the above statement: given a hermitian (resp. unitary) element y in A/J, can we find a hermitian (resp. unitary) element x in A such that π(x)=y? (The author has learned that this question, in a more restrictive form, was raised by F. F. Bonsall and that some special cases were investigated; see [1], [2].) In the present note, we give a partial answer to this question under the assumption that A is finite dimensional.

On Some Invariants of a Bilinear Form

1961 ◽  
Vol 4 (3) ◽  
pp. 261-264
Author(s):  
Jonathan Wild
Keyword(s):  
Vector Space ◽  
Bilinear Form ◽  
Arbitrary Field ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Special Cases ◽  
Orthogonal Subspace

Let E be a finite dimensional vector space over an arbitrary field. In E a bilinear form is given. It associates with every sub s pa ce V its right orthogonal sub space V* and its left orthogonal subspace *V. In general we cannot expect that dim V* = dim *V. However this relation will hold in some interesting special cases.

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