Counterexamples concerning topologization of spaces of strongly almost convergent sequences
Keywords: modulus function, sequence space, AK-space, F-seminorm, F-norm, paranorm, strong almos convergence
Let λ be a sequence space, f a modulus function, and F=(fk) a sequence of moduli. We characterize the F-normability of the sequence space λ(F) for λ⊂l∞. In the special case if λ is the space sac0 of strongly almost convergent to zero sequences, we give two counterexamples concerning the topologization of various extensions of sac0(F) and sac0(f) considered by Nanda and others. We also correct a similar inaccuracy in a previous paper of the author.
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