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Abstract
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Let X be a refexive separable Banach space, and let pB the set of
p-Bessel sequences in X^* for X. We show that pB is a non-commutative unital
Banach algebra isometrically isomorphic to B(X). Also, we classify p-Bessel
sequences for X in terms of different kind of operators in B(X) and B(X), and
we give important characterizations of p-frames and q-Riesz sequences. Using
an isomorphism between the sets pB and B(X) we obtain interesting results
for p-frames in Banach spaces. Using operator theory tools, we investigate the
geometry of p-Bessel sequences. Also, we show that the set of all q-Riesz bases
for X^* is a topological group.
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