  We present a multi wavelength analysis of 28 of the most luminous
low-redshift narrow-line, ultra-hard X-ray selected active galactic nuclei
(AGN) drawn from the 70 month Swift/BAT all-sky survey, with bolometric
luminosities of log(L_bol/erg/s) > 45.25. The broad goal of our study is to
determine whether these objects have any distinctive properties, potentially
setting them aside from lower-luminosity obscured AGN in the local Universe.
Our analysis relies on the first data release of the BAT AGN Spectroscopic
Survey (BASS/DR1) and on dedicated observations with the VLT, Palomar, and Keck
observatories. We find that the vast majority of our sources agree with
commonly used AGN selection criteria which are based on emission line ratios
and on mid-infrared colours. Our AGN are predominantly hosted in massive
galaxies (9.8 < log(M_*/M_sun) < 11.7); based on visual inspection of archival
optical images, they appear to be mostly ellipticals. Otherwise, they do not
have distinctive properties. Their radio luminosities, determined from publicly
available survey data, show a large spread of almost 4 orders of magnitude -
much broader than what is found for lower X-ray luminosity obscured AGN in
BASS. Moreover, our sample shows no preferred combination of black hole masses
(M_BH) and/or Eddington ratio (lambda_Edd), covering 7.5 < log(M_BH/M_sun) <
10.3 and 0.01 < lambda_Edd < 1. Based on the distribution of our sources in the
lambda_Edd-N_H plane, we conclude that our sample is consistent with a scenario
where the amount of obscuring material along the line of sight is determined by
radiation pressure exerted by the AGN on the dusty circumnuclear gas.
