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Center of simple non unital Banach algebra.
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What can we say about the center of a simple (it has no proper ,non zero, closed ideal), non unital Banach ( or C*- ) algebra. Given that an algebra,as usual, is a vector space (here, over the field of complex numbers) with multiplication of two elements defined in an associative way. Will it always be 0? For example , The algebra of all compact operator on a separable Hilbert space is simple and non unital. Its center is zero subspace.
functional-analysis
asked Jul 31 at 13:20
Bhuvan
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up vote
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What can we say about the center of a simple (it has no proper ,non zero, closed ideal), non unital Banach ( or C*- ) algebra. Given that an algebra,as usual, is a vector space (here, over the field of complex numbers) with multiplication of two elements defined in an associative way. Will it always be 0? For example , The algebra of all compact operator on a separable Hilbert space is simple and non unital. Its center is zero subspace.
functional-analysis
asked Jul 31 at 13:20
Bhuvan
11
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 31 at 13:23
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What can we say about the center of a simple (it has no proper ,non zero, closed ideal), non unital Banach ( or C*- ) algebra. Given that an algebra,as usual, is a vector space (here, over the field of complex numbers) with multiplication of two elements defined in an associative way. Will it always be 0? For example , The algebra of all compact operator on a separable Hilbert space is simple and non unital. Its center is zero subspace.
functional-analysis
asked Jul 31 at 13:20
Bhuvan
11
What can we say about the center of a simple (it has no proper ,non zero, closed ideal), non unital Banach ( or C*- ) algebra. Given that an algebra,as usual, is a vector space (here, over the field of complex numbers) with multiplication of two elements defined in an associative way. Will it always be 0? For example , The algebra of all compact operator on a separable Hilbert space is simple and non unital. Its center is zero subspace.
functional-analysis
asked Jul 31 at 13:20
Bhuvan
11
asked Jul 31 at 13:20
Bhuvan
11
asked Jul 31 at 13:20
Bhuvan
11
asked Jul 31 at 13:20
Bhuvan
11
11
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 31 at 13:23
add a comment |Â
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 31 at 13:23
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 31 at 13:23
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 31 at 13:23
add a comment |Â
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 31 at 13:23