  Notion of frames and Bessel sequences for metric spaces have been introduced.
This notion is related with the notion of Lipschitz free Banach spaces. \ It is
proved that every separable metric space admits a metric $\mathcal{M}_d$-frame.
Through Lipschitz-free Banach spaces it is showed that there is a
correspondence between frames for metric spaces and frames for subsets of
Banach spaces. Several characterizations of metric frames are obtained.
Stability results are also presented. Non linear multipliers are introduced and
studied. This notion is connected with the notion of Lipschitz compact
operators. Continuity properties of multipliers are discussed.
  For a subclass of approximated Schauder frames for Banach spaces,
characterization result is derived using standard Schauder basis for standard
sequence spaces. Duals of a subclass of approximate Schauder frames are
completely described. Similarity of this class is characterized and
interpolation result is derived using orthogonality. A dilation result is
obtained. A new identity is derived for Banach spaces which admit a homogeneous
semi-inner product. Some stability results are obtained for this class.
  A generalization of operator-valued frames for Hilbert spaces are introduced
which unifies all the known generalizations of frames for Hilbert spaces. This
notion has been studied in depth by imposing factorization property of the
frame operator. Its duality, similarity and orthogonality are addressed.
Connections between this notion and unitary representations of groups and
group-like unitary systems are derived. Paley-Wiener theorem for this class are
derived.
