The effective kaon mass m(K) in dense baryonic matter is calculated b
ased on PCAC, current algebra and the Weinberg smoothness hypothesis.
The off-shell behavior of the K-N scattering amplitudes is treated con
sistently with PCAC, and the effects of the subthreshold K-N resonance
s are also included. The m(K) is found to depend crucially on the K-N
sigma term, SIGMA(KN). Since the current estimates of SIGMA(KN) are v
ery uncertain, we discuss various scenarios treating SIGMA(KN) as an i
nput parameter; for certain values of SIGMA(KN) a collective mode of a
hyperon-particle-nucleon-hole state appears at high densities, possib
ly leading to kaon condensation.