After years of watching Westwood Village deteriorate into a zone of overgrown trees and empty storefronts, retailers here said they saw a glimmer of hope recently as cleaning crews began power-scrubbing the district's grimy sidewalks. A new business improvement district – Westwood's first in nearly a decade – has begun having trash picked up, freshly trimmed branches decked with lights and thousands of inky chewing-gum splotches scrubbed off the walkways.