BESSAGA'S CONJECTURE, AND QUASI-EQUIVALENCE PROPERTY IN UNSTABLE KOTHE SPACES 

 Jasser Sarsour  

Supervisor:Zafer Nurlu June 1991, 41 pages

A Kothe space E= K(anr ) satisfies QEP if and only if all unconditional bases of E are QE.                    E satisfies Bessaga's conjecture if F is a space with basis, which is isomorphic to a complemented  subspace of E, then the basis of F is QE to a subsequence of a basis of E.                    In this work we show that all unstable Kothe spaces saticfy Bessaga's conjecture and that every  complemented subspace with basis of an unstable Kothe space is an unstable Kothe space. We alsa show that  if E=E1 E2, (E1, E2)  K and Ei satisfies Bessaga's conjecture then E satisfies the conjecture under some  assumptions.                  At the end we show that if Ei A and E = Ei  then E satisfies QEP under certain conditions and  it has unique decomposition property.  Key words :  Nuclear Kothe spaces, unstable Kothe spaces, Quasi equvlence property , Bessage's conjecture, unique decomposition property.