Duality of sequence spaces of infinite matrices

52305204 : MAJOR : MATHEMATICS

KEY WORD : BANACH SPACE / DUALITY / DIRECT- SUM l¹

SUCHAT SAMPHAVAT : DUALITY OF SEQUENCE SPACES OF INFINITE MATRICES. THESIS ADVISOR : JITTI RAKBUD, Ph.D.. 31 pp.

In this thesis, we define, for each 1

d f

r , the set of infinite complex matrices as follows:

‚

r

^

^{( )}

`

₁ ^{( ) 2}

1

: :

^r

r k k

ji ji

k k

a a B

f f

­ ª º ª º l ½

‚ ® ¯ ¬ ¼ « ¬ ¦ » ¼  ¾ ¿

^.

We first show as a preliminary that equipped with the norm

^

^{( )jik}

`

_{k 1} ^: _{k 1} ^{( )jik r 1/r}

r

a ^f

ª

^f a

º

ª º ¦

¬ ¼ « ¬ » ¼

^,

the set is a Banach space. The main goal of this research is to decompose the dual

‚

r

r

‚

of as an direct- sum of its two closed subspaces by a way analogous to the classical theorem of Dixmier on decomposing the dual

‚

r l¹

B l2 of B l2 .

Department of Mathematics Graduate School, Silpakorn University

Student's signature ... Academic Year 2011

Thesis Advisor's signature ...

d

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^

^{( )}

`

₁ ^{( ) 2}

1

: :

^r

r k k

ji ji

k k

a a B

f f

­ ª º ª º l ½

‚ ® ¯ ¬ ¼ « ¬ ¦ » ¼  ¾ ¿

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^

^{( )jik}

`

_{k 1} ^: _{k 1} ^{( )jik r 1/r}

r

a ^f

ª

^f a

º

ª º ¦

¬ ¼ « ¬ » ¼

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^{B l2}

…°Š

^{B l2}

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ACKNOWLEDGEMENTS

This thesis has been completed by the involvement of people about whom I would like to mention here.

I would like to thank Dr. Jitti Rakbud, my advisor, for his valuable suggestions and excellent advices throughout the study with great attention.

I would like to thank Dr. Somjate Chaiya and Asst. Prof. Dr. Poom Kumam for their valuable comments and suggestions.

Finally, I would like to thank the centre of excellence in mathematics, the commission on higher education, Thailand, for the financial support .

f

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